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Theorem bitsand-zeros
⊦ ¬ true ∈ bits ∧ (# bits ≤ # bits0 ∨ bits0.first) ∧ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bits
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
bitsand-app-zeros
,
bitsand-cast
,
bitsand-fillsgn
,
bitsand-zeros-02
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 16
Used lemmas:
and-zero-01
,
and-rec-03
,
and-oner-01
,
and-rec
,
Used spec theorems:
Used simplifier rules:
nat
/
ls-le-simp
nat-basic2
/
s
nat-basic1
/
ref-1
list
/bitlista/
app-03
nat
/
le-num-01
list
/bitlista/
in-append
list
/bitlista/
e-02
list-last
/bitlista/
last-elim
list-last
/bitlista/
l-02
list-last
/bitlista/
bapp
nat-basic2
/
one
list
/bitlista/
Last
list
/bitlista/
in-17
list
/bitlista/
app-02-ant
list
/bitlista/
e
bitlista
/
one-01
list
/bitlista/
c-04
nat
/
lep
nat
/
not-zero
nat-basic2
/
l-02
nat-basic1
/
f
nat-basic1
/
lf-01
nat
/
lels-01
list
/bitlista/
app
list-data
/bitlista/
size-01
nat
/
lels-02
nat-basic1
/
one-01
nat-basic2
/
one-03
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
oz
list-data
/bitlista/
l
nat-basic1
/
one
list
/bitlista/
len-02
list
/bitlista/
len
list
/bitlista/
a
list
/bitlista/
e-01
list
/bitlista/
c
list-data
/bitlista/
elim-list-c