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Theorem bits2uint-split
⊦ # bits0 ≠ 0 → bits2uint(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
bits2int-split
,
bits2int-split-01
,
bits2int-zero-02
,
bits2uint-2pot
,
bits2uint-zeros-02
,
int2int-rest-01
,
uint2int-rest
,
Used by units in proved state:
intops
,
bytes
,
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 16
Used lemmas:
bits2uint-one
,
bits2uint-base
,
bits2uint-zero
,
bits2uint-rec-02
,
Used spec theorems:
list
/bitlista/
lastdiv-rew
int-pot
/
succ
Used simplifier rules:
int-mult
/
one
int-mult
/
dist-rmerge
int-basic2
/
add-in
intnat
/
nat2int
int-mult
/
eq-dist
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
eq-pos
int-basic2
/
add-c
int-basic2
/
add-a
int-basic2
/
add-zero
list-data
/bitlista/
size-01
list
/bitlista/
app
nat-basic2
/
s
nat-basic1
/
ref-1
nat-basic2
/
c
nat-basic2
/
a
intnat
/
n2i-add
list
/bitlista/
a
list
/bitlista/
len-02
list
/bitlista/
len
list-data
/bitlista/
l