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Theorem bitsor-bi-sgn
⊦ bits ≠ [] ∧ bits0 ≠ [] → bits2int(bitsor(sgn(bits), bits0)) = bits2int(bitsor(bits, bits0))
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: 50
Proof steps: 109
Used lemmas:
bitsor-empty
,
bitsor-com
,
bitsor-first
,
bitsor-first-02
,
bitsor-first-01
,
bitsor-sgn-in
,
bitsor-bi-ones
,
bitsor-bi-zeroes
,
bitsor-zerol
,
or-rec-04
,
or-rec-03
,
or-rec-02
,
or-rec-01
,
or-rec
,
Used spec theorems:
bitopsaux
/
sgn-last-03
bitopsaux
/
sgn-base-04
bitopsaux
/
sgn-in
int2bits
/
bits2int-ones
int2bits
/
bits2int-rec-03
int2bits
/
bits2int-rec
int2bits
/
bits2int-rec-false
Used simplifier rules:
int2bits
/
bits2int-zero
int2bits
/
bits2uint-mone
int-abs
/
numadd-01
int-mult
/
two-zero
int-mult
/
succ-rmerge
int-basic2
/
mone-02
list
/bitlista/
Nil
int2bits
/
bits2int-pos
list
/bitlista/
c-08
bitopsaux
/
sgn-first
int-basic2
/
add-in
int-mult
/
eq-pos
int-mult
/
associativity
int-mult
/
commutativity
int-basic2
/
add-a
int-basic2
/
add-c
list
/bitlista/
in-14
list-data
/bitlista/
elim-list-c
int2bits
/
bits2int-ones
nat-basic2
/
s
nat-basic1
/
ref-1
bitopsaux
/
sgn-not-empty-01
list-last
/bitlista/
last-def
list-last
/bitlista/
butlast-def
nat-basic2
/
oz
nat-basic2
/
one-03
list
/bitlista/
in-append
list
/bitlista/
in-06
list
/bitlista/
in-10
list
/bitlista/
app-02-ant
list
/bitlista/
in-17
list
/bitlista/
e-01
bitopsaux
/
sgn-append
list
/bitlista/
c
list-data
/bitlista/
elim-list
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
one
list
/bitlista/
len
list
/bitlista/
a
list
/bitlista/
e-02
list-last
/bitlista/
last-elim
list
/bitlista/
Last
bitopsaux
/
sgn-empty-01
int2bits
/
bits2int-sgn
int2bits
/
bits2int-inj
int2bits
/
bits2int-one
list
/bitlista/
len-02
list
/bitlista/
c-04
bitopsaux
/
sgn-one
list
/bitlista/
e
bitlista
/
one-01
bitlista
/
one-02
list-data
/bitlista/
l
nat-basic1
/
one