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Theorem band-011x-is-lastn
⊦ i→n(i) ≤ # int2bits(j) ∧ 0 < i → band(j, 2 ^ i - 1) = bits2uint(lastn(i→n(i), int2bits(j)))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
band-011x-is-unsigned-fix
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 18
Used lemmas:
add-ones-lelen-01
,
and-one
,
bitsand-first-samesize
,
bitsand-app-false
,
band-def
,
band-011x-is-unsigned-03
,
Used spec theorems:
list
/bitlista/
split-rest
list-del
/bitlista/
lastN-append-01
Used simplifier rules:
bitlista
/
inmklist-01
list-last
/bitlista/
mk-empty
nat-basic1
/
lf-02
int-basic1
/
irref
nat-basic2
/
one
int2bits
/
bits2int-pos
list
/bitlista/
c-07
nat-basic1
/
one
nat-basic2
/
one-03
list-data
/bitlista/
size-01
intnat
/
abs-zero
list
/bitlista/
app
int2bits
/
bits2uint-base
list
/bitlista/
in-15
list-last
/bitlista/
mk-zero
int2bits
/
bits2int-zero
nat-basic2
/
oz
nat-basic2
/
eq
nat
/
let
nat-basic2
/
eq-01
list
/bitlista/
c
list-data
/bitlista/
elim-list-c
nat
/
lels-03
list-del
/bitlista/
lastN-rest-01
nat
/
lels-01
intnat
/
labs
nat-basic2
/
s
nat
/
ler
nat-basic1
/
lf-01
list
/bitlista/
e-01
list
/bitlista/
len-02
list-last
/bitlista/
mk-len
nat
/
lels
nat
/
eq
list
/bitlista/
app-02-ant
list
/bitlista/
e
list
/bitlista/
c-08
nat
/
lep
list
/bitlista/
a
list
/bitlista/
len
nat
/
eqle-one
nat
/
succ-01
nat-basic1
/
neq-01
nat-basic1
/
ls-02
nat-basic2
/
a
nat-basic2
/
c
int2bits
/
int2bits-2pot-02
int-abs
/
lels-01
int-basic1
/
ls-01
int2bits
/
int2bits-not-empty
list-data
/bitlista/
l
nat-basic1
/
f
nat
/
lels-02
int-abs
/
lels
int-abs
/
lels-03
int-abs
/
ler
int-abs
/
abs-16
intnat
/
labs-01
list-del
/bitlista/
lastN-all
int-abs
/
forward-le-05