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Theorem int2bits-lslen-06
⊦ 0 < i → (m < # int2bits(i) ↔ ¬ i < 2 ^ (n→i(m) - 1))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bits-len-mod2pot
,
int2bits-lslen-11
,
uint2bits-len-add
,
Used by units in proved state:
intops
,
bytes
,
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 3
Proof steps: 10
Used lemmas:
int2bits-eq
,
int2bits-first-02
,
int2bits-not-empty
,
int2bits-lslen-01
,
Used spec theorems:
intnat
/
rax-01
Used simplifier rules:
nat
/
lez-01
nat-basic2
/
one
nat-basic2
/
oz
nat-basic2
/
l
nat-basic1
/
ref-1
nat
/
elim-pred-c
nat-basic1
/
lf-01
nat
/
lels-01
list
/bitlista/
a
list
/bitlista/
app
list
/bitlista/
c
list-data
/bitlista/
lf-01
nat-basic1
/
lf-02
nat-basic1
/
one
intnat
/
n2n
nat
/
pred-03
nat
/
lels-02
nat
/
ls-02
nat
/
lep-01
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
s
nat-basic1
/
f
nat
/
fle
nat
/
lels
int-abs
/
lels
int-abs
/
lels-03
int-abs
/
sub-le-01
int-abs
/
leone
intnat
/
num-n2i-ls-02
nat-basic1
/
z
list-data
/bitlista/
l
int-basic1
/
ls-01