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Theorem bitsand-cast-01
⊦ bits ≠ [] ∧ bits0 ≠ [] → lastn(n, fillsgn(n, bitsand(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:
cast-law-and-one
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 31
Proof steps: 57
Used lemmas:
and-notempty-01
,
bitsand-len-true
,
bitsand-len-false
,
bitsand-app
,
and-com
,
bitsand-app-true
,
bitsand-app-false
,
bitsand-fillsgn
,
Used spec theorems:
bitopsaux
/
fill-length
list
/bitlista/
split-rest
list-del
/bitlista/
lastN-append
list-del
/bitlista/
lastN-all
bitopsaux
/
fillsgn-longer
Used simplifier rules:
list-del
/bitlista/
lastN-append
nat
/
lels-02
list
/bitlista/
c-08
nat
/
ls-le-simp
list
/bitlista/
app-02-ant
list
/bitlista/
e
nat
/
succ-01
list
/bitlista/
len-02
list
/bitlista/
e-01
list
/bitlista/
c
list-data
/bitlista/
elim-list
nat
/
ler
nat
/
let
nat-basic2
/
l
nat-basic1
/
trans-1
nat
/
fle
nat-basic1
/
trans
nat-basic2
/
succ
nat-basic1
/
ref-1
nat-basic2
/
l-02
nat-basic1
/
lf-01
list-data
/bitlista/
size-01
list
/bitlista/
app
bitopsaux
/
fill-zero
list-del
/bitlista/
lastN-zero
nat-basic2
/
l-01
nat-basic1
/
lf-02
list-data
/bitlista/
l
nat
/
lels
nat
/
le-ls-simp
list
/bitlista/
Nil
nat-basic2
/
c
nat-basic2
/
a
nat
/
lep
list
/bitlista/
a
list
/bitlista/
len
nat-basic1
/
ls-02
nat-basic1
/
f
nat
/
lels-01