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Theorem bits2uint-inv-neg
⊦ bits ≠ [] ∧ ¬ bits.first → bits2uint(bitsinvert(bits)) = 2 ^ n→i(# bits) + ~ bits2int(bits) - 1
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2int-lastn-negpos
,
int2uint-pos
,
Used by units in proved state:
bytes
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 18
Used lemmas:
bits2uint-base
,
bits2uint-zero
,
bits2uint-one
,
bits2uint-rec-01
,
bits2int-pos-02
,
Used spec theorems:
int-pot
/
Pot-pos
Used simplifier rules:
bitopsaux
/
inv-false
int-basic2
/
pred
int-mult
/
eq-pos
int-abs
/
numls-02
int-abs
/
mone-06
intnat
/
nat2int
list
/bitlista/
first-01
bitopsaux
/
invert-base
list-data
/bitlista/
size-01
nat-basic2
/
s
nat-basic1
/
ref-1
list
/bitlista/
e-02
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
succ-rmerge
int-mult
/
dist-rmerge
bitopsaux
/
inv-one-01
bitopsaux
/
inv-append
nat-basic2
/
c
nat-basic2
/
a
intnat
/
n2i-add
list
/bitlista/
a
list
/bitlista/
len-02
list
/bitlista/
len
list-last
/bitlista/
last-elim
int-abs
/
sub-eq
int-abs
/
sub-sub
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
neg-15