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Theorem bitsand-app-zeros
⊦ ¬ true ∈ bits → sgn(bitsand(bits + false ' + bits0, false ' + bits1)) = sgn(bitsand(false ' + bits0, false ' + bits1))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
bitsand-cast-04
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 23
Proof steps: 46
Used lemmas:
and-notempty
,
bitsand-onein
,
and-notempty-05
,
bitsand-zero-in
,
bitsand-zeros-01
,
and-rec-06
,
bitsand-zeros
,
and-zero-01
,
and-rec-02
,
and-rec-01
,
and-rec
,
Used spec theorems:
bitopsaux
/
sgn-append-04
bitopsaux
/
sgn-last-both
Used simplifier rules:
list
/bitlista/
app-03
list
/bitlista/
e-03
list
/bitlista/
Nil
list
/bitlista/
in-06
list-last
/bitlista/
last-01
list-last
/bitlista/
lapp-01
list-last
/bitlista/
butlast-def
list-last
/bitlista/
bin
nat-basic2
/
z-01
nat
/
add-num-03
list
/bitlista/
e-02
list-last
/bitlista/
last-elim
list-last
/bitlista/
l-02
list-last
/bitlista/
bapp
nat-basic2
/
one
list
/bitlista/
e-01
bitopsaux
/
sgn-two
bitopsaux
/
sgn-mklist-02
list-last
/bitlista/
mk-zero
bitlista
/
mklist-num
list-last
/bitlista/
mk-plus
list-last
/bitlista/
lb
nat
/
lels
nat
/
fle
nat-basic2
/
s
nat-basic1
/
one-01
nat
/
ls-01
nat-basic1
/
ref-1
list
/bitlista/
Last
nat-basic1
/
f
list
/bitlista/
c-08
nat
/
lels-01
nat
/
lep-02
list
/bitlista/
in-17
list
/bitlista/
in-append
bitopsaux
/
sgn-zero
list
/bitlista/
c-04
bitopsaux
/
sgn-one
list
/bitlista/
app
list
/bitlista/
app-04
list
/bitlista/
e
list
/bitlista/
app-02-ant
list
/bitlista/
c-03
list-data
/bitlista/
l
nat-basic2
/
one-03
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
oz
nat-basic1
/
one
list
/bitlista/
a
list
/bitlista/
len-02
list
/bitlista/
len