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Theorem int2int-rest-01
⊦ j < ~1 → bits2int(int2bits(j).rest) = j + 2 ^ (n→i(# int2bits(j)) - 1)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
intops
,
bytes
,
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 13
Used lemmas:
bits2uint-one-03
,
bits2uint-zeros-03
,
bits2uint-split
,
int2uint-neg
,
bits2int-pos
,
int2bits-truein
,
uint2bits-one
,
int2bits-neg-num
,
int2bits-exneg
,
Used spec theorems:
list
/bitlista/
c-07
int-pot
/
pot-dist-pos
Used simplifier rules:
intnat
/
nat2int
int-pot
/
succ
int-mult
/
numeq
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
one
nat-basic2
/
oz
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
numsub
nat-basic2
/
c
nat-basic2
/
a
intnat
/
n2i-add
list
/bitlista/
len
list
/bitlista/
in-13
list
/bitlista/
in-14
int-basic1
/
numlsf
int-abs
/
lels
int-abs
/
mone-08
list
/bitlista/
Two
bitopsaux
/
invert-zero
bitopsaux
/
inv-one-01
list
/bitlista/
c
list
/bitlista/
a
bitopsaux
/
succ-zero
list
/bitlista/
Last
bitopsaux
/
sgn-two-01
list
/bitlista/
rest
list
/bitlista/
len-02