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Theorem or-invandinv
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsor(bits, bits0) = bitsinvert(bitsand(bitsinvert(bits), bitsinvert(bits0)))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
bor-2pot-plus
,
bor-2pot-plus-01
,
bor-notAndNot
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 15
Proof steps: 34
Used lemmas:
and-rec
,
and-rec-02
,
and-rec-01
,
and-rec-04
,
and-rec-03
,
or-rec-04
,
or-rec-03
,
or-rec-02
,
or-rec-01
,
or-rec
,
Used spec theorems:
Used simplifier rules:
nat-basic2
/
s
nat-basic1
/
ref-1
nat-basic2
/
one
list
/bitlista/
app-03
list-last
/bitlista/
last-def
list-last
/bitlista/
butlast-def
list
/bitlista/
len
bitopsaux
/
inv-len
list
/bitlista/
len-02
nat-basic2
/
oz
nat-basic2
/
a
nat-basic2
/
c
nat-basic2
/
one-03
list
/bitlista/
first-01
bitopsaux
/
invert-base
list
/bitlista/
Nil
list
/bitlista/
e-02
list-last
/bitlista/
last-elim
list
/bitlista/
Last
bitopsaux
/
inv-true-01
bitopsaux
/
inv-one-01
bitopsaux
/
inv-inv
bitopsaux
/
inv-empty
list
/bitlista/
first
list
/bitlista/
c-04
list
/bitlista/
e
bitopsaux
/
inv-false
list
/bitlista/
c-03
list
/bitlista/
e-01
bitopsaux
/
inv-append
bitopsaux
/
inv-one
list-data
/bitlista/
elim-list-c
list
/bitlista/
a
list
/bitlista/
app
list
/bitlista/
c
list-data
/bitlista/
lf-01
list-data
/bitlista/
l
nat-basic1
/
one