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Theorem band-min
⊦ i0 ≤ ~(2 ^ n→i(# int2bits(i))) ∧ # int2bits(i) = # int2bits(j) ∧ i ≤ 0 ∧ j ≤ 0 → ¬ 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:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 37
Proof steps: 78
Used lemmas:
and-notempty-09
,
and-rec
,
and-onel-01
,
and-zero-02
,
band-def
,
Used spec theorems:
int2bits
/
int2bits-rec-neg-01
int2bits
/
int2bits-mod2-len
int2bits
/
int2bits-rec-neg
int2bits
/
int2bits-mone
int2bits
/
bits2int-rec-false
int2bits
/
bits2int-rec-true
int-abs
/
numls-03
int-div
/
nummult-ls-01-01
int-mult
/
commutativity
int-div
/
nummult-ls-01
int-abs
/
num-eq-shift
int-abs
/
zero-ge-01
int-pot
/
succ
Used simplifier rules:
int-mult
/
modzero-08
int-mult
/
numls-03
int-div
/
div-lezero
int-abs
/
neg
int-mult
/
minus-one-01
int-mult
/
numls-07
int-abs
/
numle-02
int-mult
/
numle-12
int-abs
/
neg-01
int-div
/
neg-01
int-div
/
abs
int-abs
/
lep-01
int-pot
/
two-lez-01
intnat
/
nat2int-06
int-mult
/
dist-rmerge
int-mult
/
modzero
intnat
/
nat2int
int-pot
/
pot2-pos
int-abs
/
lels-04
int-basic1
/
ls-01
int-abs
/
zero-gels-04
int-abs
/
forward-lele
int-abs
/
forward-le-01
int-div
/
nummult-ls-01
int-abs
/
zero-gels-01
int-mult
/
zero-ls
int-abs
/
numlsledel
int-abs
/
Abs-pos
int-abs
/
minus-add
int-mult
/
minus-left
int-abs
/
sub-add-01
int-abs
/
sub-eq
int-abs
/
numsub
int-basic2
/
add-zero
int-mult
/
eq-same
int-abs
/
neg-10
int-mult
/
numls-09
int-abs
/
numls-02
int-abs
/
mone-06
int-mult
/
ls-same-02
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
one
int-mult
/
pred-rmerge
int-abs
/
neg-15
int-abs
/
abs-06
int-basic2
/
ls-02
int-basic2
/
ls-01
int-abs
/
neg-07
int-abs
/
subsub
int-abs
/
abs-08
int-abs
/
abs-05
intnat
/
labs
int-abs
/
sub-ls-01
int-abs
/
sub-ls
int-abs
/
lsone
int-abs
/
lels-01
int-abs
/
forward-le-05
int-abs
/
forward-lels
int-basic2
/
ls
int-pot
/
two-lsz
int-div
/
div-elim-negpos
list
/bitlista/
Last
list-last
/bitlista/
last-def
list-last
/bitlista/
butlast-def
nat-basic2
/
one
nat-basic1
/
one
nat-basic2
/
oz
intnat
/
n2i-add
nat-basic2
/
eq-01
int-abs
/
numadd-01
int-basic2
/
mone-02
nat-basic2
/
c
nat-basic2
/
a
list-data
/bitlista/
l
nat-basic2
/
one-03
int-abs
/
mone-05
int-abs
/
lels-03
int-abs
/
numlelsdel
int-abs
/
numls-03
int-abs
/
elim-sub
int-basic1
/
numlslsdel
list
/bitlista/
a
list
/bitlista/
len
int-abs
/
mone-08
int2bits
/
int2int-inj
int-abs
/
forward-le-02
int-abs
/
lels-02
int2bits
/
int2bits-not-empty
int2bits
/
bits2int-zero
int-basic1
/
numlsf
int-abs
/
zero-gels-03
int-abs
/
forward-lsle
int-abs
/
forward-le-03
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
numle-03
list
/bitlista/
len-02
int2bits
/
int2bits-zero
int-abs
/
anti
int-abs
/
lels
int-abs
/
forward-le-04
int-abs
/
negle-07