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Theorem and-ass
⊦ bits ≠ [] ∧ bits0 ≠ [] ∧ bits1 ≠ [] → bitsand(bits, bitsand(bits0, bits1)) = bitsand(bitsand(bits, bits0), bits1)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
band-associativity
,
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:
bitsand-onel
,
bitsand-zerol
,
and-notempty
,
and-rec-02
,
and-rec-01
,
and-oner-01
,
and-zero-03
,
and-zero-02
,
and-rec-03
,
and-rec
,
Used spec theorems:
Used simplifier rules:
list
/bitlista/
app-02-ant
list
/bitlista/
e
list
/bitlista/
app-01
list-last
/bitlista/
last-elim
list
/bitlista/
e-02
nat-basic2
/
one-03
list
/bitlista/
c-05
list
/bitlista/
first-01
list
/bitlista/
app
list
/bitlista/
c
list-data
/bitlista/
lf-01
list-data
/bitlista/
l
nat-basic2
/
one
nat-basic2
/
oz
nat-basic1
/
one
list
/bitlista/
Last
list-last
/bitlista/
last-def
list-last
/bitlista/
butlast-def
list
/bitlista/
app-06
list
/bitlista/
Nil
list
/bitlista/
first
list
/bitlista/
c-04
list
/bitlista/
len
list
/bitlista/
len-02
list
/bitlista/
a
nat-basic2
/
s
nat-basic1
/
ref-1
nat-basic2
/
a
nat-basic2
/
c