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Theorem add-ones-grlen
⊦ ¬ false ∈ bits ∧ # bits0 ≤ # bits ∧ bits0.first ∧ bits0 ≠ [] → bitsand(bits, bits0) = fillsgn(# bits, bits0)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
add-ones-grlen-01
,
bitsand-cast
,
bitsand-fillsgn
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 19
Used lemmas:
and-rec-01
,
and-onel-02
,
and-oner-01
,
and-rec
,
Used spec theorems:
Used simplifier rules:
bitopsaux
/
fill-fill
list-last
/bitlista/
mk-last
nat
/
elim-sub
nat-basic2
/
l-02
nat-basic1
/
lf-01
nat
/
succ-01
nat-basic1
/
z
nat-basic2
/
one-03
bitlista
/
mklist-01
list-last
/bitlista/
mk-empty
list
/bitlista/
app-05
list
/bitlista/
app-01
list
/bitlista/
in-empty
nat
/
lez-01
nat-basic2
/
z-01
nat
/
lez
nat-basic2
/
z
list-data
/bitlista/
size-01
list
/bitlista/
c-03
nat-basic2
/
one
nat-basic2
/
oz
list
/bitlista/
app
list-data
/bitlista/
lf-01
nat-basic1
/
one
list
/bitlista/
Last
list-data
/bitlista/
elim-list-c
list
/bitlista/
in-06
nat
/
lels
list-last
/bitlista/
l-02
list-last
/bitlista/
bapp
list
/bitlista/
e-01
list
/bitlista/
app-04
list
/bitlista/
c
list-last
/bitlista/
last-elim
list
/bitlista/
app-03
list
/bitlista/
in-17
list
/bitlista/
in-append
nat
/
lep-02
list
/bitlista/
e-02
list
/bitlista/
app-02-ant
list
/bitlista/
e
list
/bitlista/
in-10
nat-basic2
/
eq-01
nat
/
fle
nat-basic1
/
lf-02
nat-basic1
/
f
nat
/
fle-01
list-data
/bitlista/
l
list
/bitlista/
len
list
/bitlista/
len-02
list
/bitlista/
a
nat-basic2
/
s
nat-basic1
/
ref-1
nat-basic2
/
a
nat-basic2
/
c