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Theorem bits2int-split-01
⊦ # bits0 ≠ 0 ∧ # bits ≠ 0 ∧ bits.first → bits2int(bits + bits0) = ~(2 ^ n→i(# bits0) * bits2uint(bitsinvert(bits))) - bits2uint(bitsinvert(bits0)) + 1
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2int-lastn-negneg
,
int2int-lastn-negpos
,
Used by units in proved state:
intops
,
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 16
Used lemmas:
bits2uint-ones
,
bits2uint-zeros
,
bits2uint-succ
,
bits2uint-split
,
bits2uint-zeros-03
,
bits2int-neg
,
Used spec theorems:
bitopsaux
/
succ-zeros
bitopsaux
/
succ-len
Used simplifier rules:
int-abs
/
numadd-01
int-abs
/
negeq
int-abs
/
subsub
list-data
/bitlista/
elim-list-c
int-abs
/
mone-01
int-abs
/
sub-eq
int-abs
/
sub-add-01
int-abs
/
neg-15
bitopsaux
/
inv-append
bitopsaux
/
invert-one
bitopsaux
/
succ-zero-02
bitopsaux
/
succ-empty-01
int-basic2
/
add-in
bitopsaux
/
succ-ones
bitopsaux
/
inv-inv
list
/bitlista/
c
list
/bitlista/
len
list
/bitlista/
len-02
intnat
/
n2i-add
nat-basic2
/
a
nat-basic2
/
c
list-data
/bitlista/
l
int-basic2
/
add-zero
list
/bitlista/
app-02-ant
list
/bitlista/
e
list
/bitlista/
e-01
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
one
int-mult
/
eq-dist
list
/bitlista/
a
bitopsaux
/
inv-len
int-abs
/
Sub-def
int-basic2
/
add-a
int-basic2
/
add-c
bitopsaux
/
inv-in-01
bitopsaux
/
inv-empty