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Theorem bitsand-cast-04
⊦ # bits0 ≤ n ∧ ¬ bits0.first ∧ bits ≠ [] ∧ bits0 ≠ [] → sgn(bitsand(lastn(n, fillsgn(n, bits)), bits0)) = sgn(bitsand(bits, bits0))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
bitsand-cast-05
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 19
Proof steps: 44
Used lemmas:
bitsand-app-zeros
,
and-com
,
bitsand-app-ones
,
bitsand-app-false
,
Used spec theorems:
bitopsaux
/
fillsgn-longer
bitopsaux
/
fill-fill
list-del
/bitlista/
lastN-all
list
/bitlista/
split-rest
list-del
/bitlista/
lastn-app
Used simplifier rules:
nat
/
eq
bitlista
/
inmklist
nat
/
ls-le-simp
bitlista
/
inmklist-01
nat
/
fle
nat
/
eqle-one
nat-basic1
/
neq-01
nat
/
lels-02
nat
/
lep-02
list
/bitlista/
app-02-ant
list
/bitlista/
e
list
/bitlista/
c-08
nat-basic1
/
lf-02
nat-basic1
/
lf-01
list-data
/bitlista/
l
nat
/
ler
nat
/
lep
nat
/
let
list-last
/bitlista/
mk-len
nat-basic2
/
eq-01
nat
/
lels
nat-basic2
/
s
nat-basic2
/
l-01
nat
/
elim-sub
nat
/
lels-03
nat-basic1
/
ls-02
nat
/
lels-01
nat-basic1
/
f
nat-basic2
/
c
nat-basic2
/
a
nat
/
succ-01
list
/bitlista/
len-02
list
/bitlista/
len
list
/bitlista/
a
list
/bitlista/
e-01
list
/bitlista/
c
list-data
/bitlista/
elim-list-c