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Theorem bitsand-cast
⊦ bits ≠ [] ∧ bits0 ≠ [] → lastn(n, fillsgn(n, bitsand(sgn(lastn(n, fillsgn(n, bits))), bits0))) = lastn(n, fillsgn(n, bitsand(bits, bits0)))
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: 384
Proof steps: 735
Used lemmas:
add-ones-lelen-01
,
and-zero-02
,
and-onel-01
,
bitsand-zeros-01
,
bitsand-zeros
,
and-notone
,
and-notempty
,
bitsand-len-false
,
and-notempty-01
,
bitsand-len-true
,
add-ones-grlen-02
,
add-ones-grlen
,
add-ones-lelen
,
bitsand-app
,
and-com
,
and-first
,
and-notempty-02
,
bitsand-app-true
,
bitsand-app-false
,
Used spec theorems:
bitopsaux
/
fill-lastn-01
list-last
/bitlista/
mk-plus
bitopsaux
/
sgn-ex-01
list-last
/bitlista/
mk-last-02
list-del
/bitlista/
lastn-mklist
list
/bitlista/
first-01
list-del
/bitlista/
lastn-app
list
/bitlista/
a
bitopsaux
/
sgn-mklist-03
list-del
/bitlista/
lastN-append-01
bitopsaux
/
sgn-zero
bitopsaux
/
fill-rec-one
list
/bitlista/
split-rest
bitopsaux
/
fillsgn-longer
list-del
/bitlista/
lastN-append
list-del
/bitlista/
lastN-all
bitopsaux
/
fill-length
bitopsaux
/
fill-fill
list-last
/bitlista/
mk-first-01
bitlista
/
mklist-intro
Used simplifier rules:
bitlista
/
mklist
bitopsaux
/
sgn-empty
bitopsaux
/
fill-zero
list-del
/bitlista/
lastN-zero
bitopsaux
/
fillsgn-longer
list-last
/bitlista/
mk-in
nat-basic1
/
neq-01
nat
/
anti
nat
/
lez-01
nat
/
add-01
bitopsaux
/
fillsgn-empty
nat
/
lels-02
list-del
/bitlista/
lastN-append
bitopsaux
/
fill-size
bitlista
/
mklist-num
list
/bitlista/
c-06
list-data
/bitlista/
elim-list
list-del
/bitlista/
lastN-all
list-del
/bitlista/
lastn-mklist-03
bitopsaux
/
sgn-zero
nat-basic1
/
z
nat
/
sub-base
bitlista
/
mklist-01
bitopsaux
/
sgn-true
bitopsaux
/
sgn-zeros
nat
/
ls-le-simp
nat
/
let
bitopsaux
/
fill-nls
nat
/
l-num-02
bitopsaux
/
fill-lastn
bitopsaux
/
sgn-base-02
nat-basic2
/
eq-01
list-last
/bitlista/
mk-first
nat
/
lep
list
/bitlista/
first-01
bitopsaux
/
fill-fill
bitopsaux
/
sgn-base-01
nat-basic2
/
z-01
list-data
/bitlista/
size-01
nat
/
ler
nat
/
lels
nat-basic1
/
ref-1
nat
/
add-num-03
nat-basic1
/
lf-02
list-del
/bitlista/
lastN-append-01
nat-basic2
/
l-02
nat
/
eq-01
list-del
/bitlista/
lastn-mklist
nat-basic2
/
l-08
nat-basic2
/
succ
nat-basic1
/
trans-1
nat-basic1
/
trans
list-data
/bitlista/
l
nat-basic2
/
one
nat
/
eq-02
nat
/
fle
list-last
/bitlista/
mk-inj-01
bitopsaux
/
sgn-in-02
nat
/
fle-01
list
/bitlista/
app
nat-basic2
/
z
list
/bitlista/
Nil
list-last
/bitlista/
mk-zero
list-last
/bitlista/
mk-first-01
list
/bitlista/
app-01
nat-basic2
/
l-01
nat
/
cancel-01
list-last
/bitlista/
mk-plus
nat
/
lep-02
nat
/
elim-sub
list
/bitlista/
app-03
nat-basic2
/
oz
nat-basic2
/
l
nat
/
elim-pred-c
list-last
/bitlista/
mk-empty
nat
/
le
nat-basic1
/
one-01
list
/bitlista/
e-01
list
/bitlista/
c-08
list
/bitlista/
app-02-ant
list
/bitlista/
e
nat
/
lels-03
nat-basic2
/
a
nat
/
prop-07
nat
/
le-ls-simp
nat-basic2
/
c
bitlista
/
inmklist
bitlista
/
inmklist-01
nat
/
pred-03
list
/bitlista/
len-02
list-last
/bitlista/
mk-len
list
/bitlista/
len
list
/bitlista/
in-17
list
/bitlista/
in-append
list
/bitlista/
e-03
list
/bitlista/
in-13
list
/bitlista/
a
list
/bitlista/
in-14
list
/bitlista/
c
nat-basic1
/
lf-01
bitopsaux
/
sgn-fill
nat-basic1
/
ls-02
nat-basic1
/
f
nat
/
lels-01