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Theorem int2int-lastn-posneg
⊦ 0 < i ∧ lastn(m, int2bits(i)).first ∧ m ≤ # int2bits(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:
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 17
Used lemmas:
ubits2bits
,
bits2uint-nle-01
,
int2bits-first
,
bits2uint-not-neg-01
,
bits2uint-zeros-03
,
int2bits-first-03
,
bits2int-split
,
int2bits-first-02
,
int2int-inj
,
int2bits-not-empty
,
Used spec theorems:
list-del
/bitlista/
lastN-ex
int-div
/
modeq-pos
Used simplifier rules:
list-del
/bitlista/
lastN-empty
int-mult
/
succ-rmerge
int-basic2
/
add-in
int-abs
/
forward-lels
int-basic2
/
add-a
int-mult
/
associativity
int-mult
/
zero-ge-add
nat
/
lels-01
nat-basic1
/
ref-1
int-basic1
/
trans
int-basic1
/
lf-01
int-basic1
/
lf-03
int-basic2
/
add-c
int-mult
/
commutativity
int-abs
/
lels
int-abs
/
lels-01
list
/bitlista/
in-14
list
/bitlista/
e-01
list
/bitlista/
len-02
list
/bitlista/
len
list
/bitlista/
c
list-data
/bitlista/
elim-list-c
int-basic1
/
lf-02
list-del
/bitlista/
lastn-length-01
list-data
/bitlista/
size-01
nat
/
zero-02
list
/bitlista/
Nil
list
/bitlista/
a
list-data
/bitlista/
l
int-basic1
/
ls-01
int-abs
/
sub-eq