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Theorem band-011x-neg-01
⊦ j < 0 ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = (j + 1) % 2 ^ n→i(# int2bits(i) - 1) + 2 ^ n→i(# int2bits(i) - 1) - 1
Type: A user defined theorem
Validity: The proof is valid.
Features: localsimp,
Comment:
Used by:
band-011x-eq
,
band-011x-neg-02
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 1
Proof steps: 2
Used lemmas:
band-commutativity
,
band-associativity
,
band-011x-neg
,
Used spec theorems:
int2bits
/
int2bits-falsein-02
Used simplifier rules:
int-abs
/
zero-gels-01
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-abs
/
forward-le-01
int-abs
/
sub-eq
int-basic2
/
add-c
int-pot
/
two-minus
int-abs
/
lels-01
int2bits
/
int2bits-2pot-02
list
/bitlista/
len
list
/bitlista/
len-02
list-last
/bitlista/
mk-len
list
/bitlista/
a
nat
/
add-01
nat-basic2
/
z
nat-basic2
/
a
nat-basic2
/
c
intnat
/
ini2-abs
int-abs
/
sub-le-01
int-abs
/
leone
int-pot
/
pot2-pos
int-abs
/
absle
int-abs
/
Sub-def
int-basic2
/
add-a
int-basic2
/
add-in