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Theorem band-011x-pos-02
⊦ 0 ≤ j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = j % (i + 1)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
band-011x-eq
,
band-011x-neg-03
,
band-31-pos
,
band-63-pos
,
band-one-is-mod2
,
intshiftleft-is-mult-01
,
intshiftright-ls-01
,
intshiftrsign-rec-neg
,
intshiftrsign-rec-pos
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 2
Proof steps: 3
Used lemmas:
band-commutativity
,
band-associativity
,
band-011x-pos-01
,
Used spec theorems:
int2bits
/
int2bits-falsein-02
Used simplifier rules:
int-pot
/
two-minus
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-def
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
sub-le-01
int-abs
/
leone
int-pot
/
pot2-pos
int-abs
/
absle
int-abs
/
forward-le-01
int-abs
/
lels-01
int-abs
/
lels-04