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Theorem int2bits-rec-2pot-neg-01
⊦ j ≤ ~(2 ^ i) ∧ 0 < i ∧ j % 2 ^ i = 0 → int2bits(j) = int2bits(j / 2 ^ i) + fillsgn(i→n(i + 1), int2bits(j % 2 ^ i)).rest
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bits-rec-2pot-neg-03
,
Used by units in proved state:
intops
,
bytes
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 2
Proof steps: 4
Used lemmas:
int2bits-2pot-04
,
int2bits-zero
,
Used spec theorems:
int-div
/
modex
Used simplifier rules:
int-abs
/
lels-01
int-basic1
/
ls-01
int-mult
/
Mult-zero
list
/bitlista/
app-04
list-last
/bitlista/
mk-empty
intnat
/
abs-zero
int-mult
/
one
int-pot
/
two-lez-01
int-mult
/
succ-rmerge
int-mult
/
commutativity
int-mult
/
associativity
int-div
/
div-mult-03
list
/bitlista/
c-07
nat-basic2
/
c
nat-basic2
/
a
list-last
/bitlista/
mk-last
list
/bitlista/
a
list
/bitlista/
app
list-last
/bitlista/
mk-zero
bitlista
/
mklist-num
list-last
/bitlista/
mk-plus
bitopsaux
/
fill-one-01
int-abs
/
forward-le-05
int-abs
/
forward-le-04
int-abs
/
forward-lels
int-abs
/
negle-07
int-basic2
/
add-c
int-basic2
/
add-a
intnat
/
abs-succ-03
int-pot
/
zero