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Theorem int2bytes-rec-neg-01
j < ~(2 ^ (i * 8)), 0 < i, j % 2 ^ (i * 8) = 0 ⊦ int2bytes(j) = int2bytes(j / 2 ^ (i * 8)) + fix(i→n(i + 1), int2bytes(j % 2 ^ (i * 8))).rest
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bytes-rec-neg-03
,
int2bytes-rec-neg-256
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 14
Used lemmas:
bytes2int-zero
,
fix-pos
,
bits2bytes-mklist
,
bits2bytes-app
,
int2bytes
,
int2bytes-byte
,
Used spec theorems:
int2bits
/
int2bits-rec-2pot-neg-01
intnat
/
i2np
Used simplifier rules:
nat-basic2
/
one-03
nat-basic2
/
oz
nat-basic1
/
one
list
/bytelist/
len-02
nat
/
add-01
nat-basic2
/
z
list-last
/bytelist/
mk-last
list
/bytelist/
c-07
list-last
/bytelist/
mk-inj-01
int-abs
/
lels-02
nat-div
/
mult-01
int-mult
/
zero-eq
list
/bytelist/
a
list
/bytelist/
app-01
nat-div
/
mod-mult-01
nat-mult
/
mult-a
nat-mult
/
mult-c
int-mult
/
zero-neq-01
intnat
/
abs-zero
list-last
/bitlista/
mk-empty
int2bits
/
int2bits-not-empty
list-last
/bitlista/
mk-len
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
int2bits
/
int2bits-zero
int-abs
/
zero-gels-03
int-abs
/
negle-07
int-abs
/
lels-01
int-mult
/
commutativity
int-basic1
/
ls-01
int-mult
/
zero-gr
int-mult
/
associativity
int-abs
/
forward-le-05
int-abs
/
forward-le-02
int-abs
/
neg-07
int-basic2
/
add-c
int-basic2
/
add-a
intnat
/
abs-succ-03