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Theorem int2int-lastn-negneg
⊦ i < 0 ∧ lastn(m, int2bits(i)).first ∧ m ≤ # int2bits(i) ∧ m ≠ 0 ∧ ~ i ≠ 2 ^ n→i(m) → bits2int(lastn(m, int2bits(i))) = i % 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:
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 12
Proof steps: 23
Used lemmas:
bits2int-nle
,
bits2int-first-01
,
bits2int-first
,
bits2uint-inv-pos
,
int2bits-first
,
bits2int-split-01
,
uint2bits-one
,
int2bits-neg-num
,
int2bits-lelen-02
,
int2bits-first-01
,
int2int-inj
,
int2bits-not-empty
,
Used spec theorems:
list-del
/bitlista/
lastN-ex
int-div
/
modeq-neg
int-div
/
mod-zero-05
Used simplifier rules:
nat-basic1
/
ref-1
int-basic2
/
ls
int-abs
/
forward-lels
int-basic2
/
succ-01
int-basic1
/
trans
int-basic1
/
lf-01
int-pot
/
grz
int-abs
/
lels-01
int-abs
/
lels-03
int-abs
/
sub-add-09
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-a
int-abs
/
numadd-01
int-abs
/
subsub
list-data
/bitlista/
elim-list-c
list-del
/bitlista/
lastn-length-01
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
l-02
nat
/
lels-01
intnat
/
n2n
int-abs
/
mone-08
intnat
/
nat2int
int-basic1
/
lf-03
list
/bitlista/
Two
bitopsaux
/
invert-zero
bitopsaux
/
inv-one-01
list
/bitlista/
c
bitopsaux
/
succ-zero
list
/bitlista/
Last
bitopsaux
/
sgn-two-01
list
/bitlista/
len-02
list-del
/bitlista/
lastn-one-01
list
/bitlista/
c-04
int-abs
/
lels-02
int-basic2
/
add-c
int-abs
/
lels
int-abs
/
neg-13
int-abs
/
abs-08
nat
/
ler
list-data
/bitlista/
l
list
/bitlista/
a
list
/bitlista/
Nil
nat
/
zero-02
list-data
/bitlista/
size-01
int-abs
/
negeq