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Theorem bitsxor-is-orand
⊦ bits ≠ [] ∧ bits0 ≠ [] → bits2int(bitsxor(bits, bits0)) = bits2int(bitsor(bitsand(bitsinvert(bits), bits0), bitsand(bitsinvert(bits0), bits)))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
bxor-def-logic
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 32
Proof steps: 64
Used lemmas:
bitsxor-empty
,
bitsor-empty
,
bitsxor-rec-01
,
and-notempty
,
or-rec
,
bitsxor-rec-01-01
,
bitsxor-rec-02
,
and-onel-01
,
bitsxor-rec-04
,
or-rec-02
,
bitsxor-rec-03
,
or-rec-04
,
and-zero-02
,
and-rec-03
,
and-rec-02
,
and-rec-01
,
and-rec
,
Used spec theorems:
int2bits
/
bits2int-rec-true
int2bits
/
bits2int-rec-false
Used simplifier rules:
int2bits
/
bits2int-inj
int-basic2
/
add-in
int-mult
/
eq-pos
int-mult
/
associativity
int-mult
/
commutativity
nat-basic2
/
s
nat-basic1
/
ref-1
list
/bitlista/
Nil
list-last
/bitlista/
last-def
list-last
/bitlista/
butlast-def
nat-basic2
/
oz
nat-basic2
/
one-03
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
one
list
/bitlista/
len
bitopsaux
/
inv-one
bitopsaux
/
inv-append
list
/bitlista/
a
list
/bitlista/
e-02
list-last
/bitlista/
last-elim
list
/bitlista/
Last
bitopsaux
/
inv-false
int-abs
/
neg-15
int-abs
/
sub-add-09
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
numadd-01
int-abs
/
negeq
int-abs
/
subsub
int2bits
/
bits2int-inv
bitopsaux
/
inv-one-01
list
/bitlista/
e
list
/bitlista/
c-04
list
/bitlista/
len-02
bitopsaux
/
inv-true-01
bitlista
/
one-01
bitlista
/
one-02
bitopsaux
/
inv-empty
list-data
/bitlista/
l
nat-basic1
/
one
bitopsaux
/
inv-len