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Theorem bitsand-fillsgn
⊦ bits ≠ [] ∧ bits0 ≠ [] → fillsgn(n, bitsand(fillsgn(n, bits), bits0)) = fillsgn(n, bitsand(bits, bits0))
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
bitsand-cast-01
,
Used by units in proved state:
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 27
Proof steps: 66
Used lemmas:
and-notempty
,
bitsand-app
,
add-ones-lelen
,
add-ones-grlen
,
and-onel-01
,
bitsand-zeros
,
bitsand-zeros-01
,
and-zero-02
,
and-rec-03
,
and-rec-02
,
and-zero-03
,
and-rec-01
,
and-rec
,
Used spec theorems:
bitopsaux
/
fill-rec-one
bitopsaux
/
fillsgn-fill
bitopsaux
/
fill-last
Used simplifier rules:
list
/bitlista/
app-03
nat-basic2
/
pred
nat
/
elim-pred-c
nat
/
pred-03
list-last
/bitlista/
last-def
list-last
/bitlista/
butlast-def
nat-basic2
/
oz
nat-basic2
/
one-03
nat-basic2
/
one
list
/bitlista/
e-02
list-last
/bitlista/
last-elim
list
/bitlista/
Last
nat
/
lep-01
nat
/
eq-01
nat
/
ler
nat-basic1
/
ref-1
nat-basic2
/
z
list-data
/bitlista/
size-01
nat-basic2
/
l
nat-basic2
/
l-01
nat
/
lels-03
bitopsaux
/
fillsgn-fill
nat-basic2
/
s
bitlista
/
inmklist-01
nat-basic1
/
ls-02
list
/bitlista/
app-01
nat
/
elim-sub
nat
/
fle
nat-basic2
/
l-02
nat-basic2
/
a
list
/bitlista/
app
list-last
/bitlista/
mk-zero
bitlista
/
mklist-num
list-last
/bitlista/
mk-plus
list-last
/bitlista/
mk-inj-01
bitopsaux
/
fill-mklist
nat
/
lels-01
list
/bitlista/
c-08
list
/bitlista/
app-02-ant
nat-basic1
/
f
nat-basic2
/
c
nat
/
ls-le-simp
list
/bitlista/
len
list
/bitlista/
a
list
/bitlista/
e-01
list
/bitlista/
c
list-data
/bitlista/
elim-list-c
list-last
/bitlista/
mk-empty
nat
/
lels
list-last
/bitlista/
mk-len
bitlista
/
inmklist
nat-basic1
/
z
bitopsaux
/
fill-zero
bitopsaux
/
fill-fill-01
bitopsaux
/
fill-empty
list
/bitlista/
e
list
/bitlista/
c-04
list
/bitlista/
len-02
bitlista
/
one-01
list-data
/bitlista/
l
nat-basic1
/
one