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Theorem band-min-02
⊦ i0 ≤ ~(2 ^ (n→i(# int2bits(i)) - 1)) ∧ i0 ≤ ~(2 ^ (n→i(# int2bits(j)) - 1)) → ¬ band(i, j) < i0
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
Used by units in proved state:
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 15
Proof steps: 25
Used lemmas:
bitsand-len-true
,
and-com
,
and-notempty-09
,
band-def
,
band-notneg-01
,
band-notneg
,
band-commutativity
,
Used spec theorems:
int2bits
/
bits2int-nls-02
Used simplifier rules:
nat
/
let
nat
/
le-ls-simp
nat
/
lels
int-abs
/
le-add
int-abs
/
forward-le-05
nat-basic1
/
z
intnat
/
num-n2i-ls-02
int-abs
/
leone
int-abs
/
sub-le-01
int-pot
/
ls-pos-2pot-01
int-abs
/
sub-ls
int-abs
/
succ-02
intnat
/
le
nat
/
leprf
nat
/
fle
int-basic2
/
ls-01
int-abs
/
lels-03
int-abs
/
zero-gels-01
int-abs
/
forward-lsle
nat-basic2
/
c
nat-basic2
/
a
nat
/
sub-ls
nat
/
lels-03
int2bits
/
int2bits-first-01
nat-basic1
/
ls-02
int2bits
/
int2bits-not-empty
nat-basic1
/
f
nat
/
ls-03
nat
/
lels-01
nat-basic1
/
one-01
list-data
/bitlista/
l
int-abs
/
lels-01
int-abs
/
forward-le-02
int-abs
/
forward-le-04
int-abs
/
negle-07
int-abs
/
lels
int-abs
/
forward-lels
int-abs
/
forward-le-01
int-abs
/
forward-lele
int-abs
/
zero-gels-04
int-basic2
/
ls
int-pot
/
two-lsz
int-basic2
/
add-a
int-basic2
/
add-c