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Theorem int2bits-rec-neg
⊦ j < 0 ∧ j ≠ ~1 → int2bits(j) = int2bits((j - 1) / 2) + (~1 = j % 2)'
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bits-mod2-neg
,
int2bits-one-bit
,
int2bits-rec-neg-01
,
int2bits-rec-neg-02
,
int2bits-rec-neg-03
,
uint2bits-add-high
,
uint2bits-add-low
,
Used by units in proved state:
intops
,
bytes
,
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 11
Proof steps: 21
Used lemmas:
uint2bits-falsein
,
uint2bits-succ-intro
,
uint2bits-rec-01
,
int2bits-neg
,
Used spec theorems:
bitopsaux
/
inv-sgn
bitopsaux
/
sgn-last-diff
Used simplifier rules:
int-abs
/
sub-ls-01
int-abs
/
numls-03
bitopsaux
/
sgn-sgn-01
bitopsaux
/
inv-inv
int-abs
/
negle-07
int-abs
/
lels-01
int-basic1
/
ls-01
int-div
/
div-mult-03
int-mult
/
le-one
int-abs
/
sub-le
int-mult
/
pred-rmerge
int-abs
/
sub-sub
int-mult
/
two-zero
int-abs
/
sub-eq
int-div
/
div-sub
int-abs
/
sub-sub-04
int-abs
/
mone-01
bitopsaux
/
succ-zero
int-basic1
/
minus-one
int-abs
/
numls-02
int-abs
/
neg-13
int-abs
/
lels-02
bitopsaux
/
succ-truein-01
int-div
/
nummult-ls
int-mult
/
zero-le
int-div
/
div2-odd-01
int-mult
/
zero-ls
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
two-mone
int-basic2
/
add-zero
int-div
/
div-elim2
bitopsaux
/
succ-rec
list
/bitlista/
a
bitopsaux
/
inv-one
bitopsaux
/
inv-append
list
/bitlista/
Last
int-div
/
mod-neg-01
int-div
/
neg-01
int-abs
/
neg
int-abs
/
anti
int-abs
/
negeq
int-abs
/
numadd-01
int-basic1
/
lf-02
int-basic1
/
lf-03
int-abs
/
lsone
int-abs
/
sub-ls
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
neg-15
int-abs
/
minus-02
int-div
/
div2-neg
int-div
/
abs
int-abs
/
lels
int-div
/
div-two-zero-01
int-abs
/
sub-le-01
int-abs
/
lels-03
int-abs
/
abs-08