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Theorem band-011x-neg
⊦ j < 0 ∧ 0 ≤ i → band(j, 2 ^ i - 1) = (j + 1) % 2 ^ i + 2 ^ i - 1
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
band-011x-is-unsigned
,
band-011x-neg-01
,
band-255-neg
,
band-65535-neg
,
band-mod256-neg
,
Used by units in proved state:
bytes
,
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 20
Used lemmas:
and-011x-neg
,
and-notempty
,
and-first
,
band-commutativity
,
band-associativity
,
band-def
,
Used spec theorems:
int2bits
/
int2bits-neg
int2bits
/
bits2int-pos-02
int2bits
/
uint2bits-sgn-first
int2bits
/
int2bits-neg-01
Used simplifier rules:
int-basic2
/
add-c
int-abs
/
neg-02
int2bits
/
int2uint-inv-01
int-abs
/
subsub
int-pot
/
two-zero
int-div
/
mod-neg-01
int-abs
/
neg-15
int-abs
/
sub-add-01
int-basic2
/
add-a
intnat
/
i2i-pos-01
list-last
/bitlista/
mk-len
int-abs
/
neg
int-abs
/
lels
int-abs
/
lels-03
bitopsaux
/
sgn-in-01
bitlista
/
inmklist-01
list
/bitlista/
in-17
list
/bitlista/
in-append
int2bits
/
bits2uint-zeros-03
list
/bitlista/
in-14
list
/bitlista/
c
list-data
/bitlista/
elim-list-c
list
/bitlista/
c-08
list
/bitlista/
e-01
list
/bitlista/
app-02-ant
list
/bitlista/
e
list-last
/bitlista/
mk-empty
intnat
/
abs-zero
list
/bitlista/
a
bitopsaux
/
sgn-empty-01
bitopsaux
/
succ-empty-01
int-abs
/
abs-08
int-abs
/
forward-lsle
int-abs
/
sub-eq
int2bits
/
int2bits-2pot-02
int-abs
/
lels-01
int-abs
/
lels-04