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Theorem and-size-one
⊦ bits.first ∧ # bits ≤ # bits1 ∧ bits ≠ [] → bitsand(bits, bits0 + bits1) = bits0 + bitsand(bits, bits1)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
bor-2pot-plus
,
bor-2pot-plus-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 11
Proof steps: 26
Used lemmas:
and-rec-03
,
and-onel-01
,
and-rec
,
Used spec theorems:
list
/bitlista/
app-06
list
/bitlista/
first-01
Used simplifier rules:
list
/bitlista/
c-04
nat
/
lez
nat
/
lep-02
nat
/
fle
nat
/
fle-01
nat
/
add-01
list
/bitlista/
e-02
list-last
/bitlista/
last-elim
nat
/
ls-03
list-last
/bitlista/
b-01
list-last
/bitlista/
lb
nat-basic1
/
one-01
nat
/
lels-01
nat
/
ls-01
nat-basic1
/
ref-1
list
/bitlista/
c-03
nat-basic2
/
oz
nat-basic2
/
s
nat
/
lels
list-last
/bitlista/
b
nat-basic1
/
f
nat
/
succ-01
list-last
/bitlista/
l-02
list
/bitlista/
e-01
list
/bitlista/
app-04
list-data
/bitlista/
elim-list-c
list-last
/bitlista/
l-06
list-last
/bitlista/
lapp
list-last
/bitlista/
bapp
list
/bitlista/
Last
list
/bitlista/
app-02-ant
list-data
/bitlista/
eq-one
nat-basic2
/
z
list
/bitlista/
Nil
list-data
/bitlista/
size-01
nat
/
lez-01
list
/bitlista/
first
list
/bitlista/
len-02
list
/bitlista/
e
nat-basic2
/
one
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
z-01
list
/bitlista/
len
list
/bitlista/
a
list
/bitlista/
app
list
/bitlista/
c
list-data
/bitlista/
lf-01
list-data
/bitlista/
l
nat-basic1
/
one