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Theorem cast-size-fits-01
0 < i ⊦ ~(2 ^ (i - 1)) ≤ j ∧ j < 2 ^ (i - 1) → cast(i, j) = j
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
cast-if
,
Used by units in proved state:
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 11
Used lemmas:
cast-zero
,
cast-size-fits
,
Used spec theorems:
intnat
/
num-n2i-ls-02
int2bits
/
int2bits-lslen-06
int2bits
/
int2bits-lslen-05
int2bits
/
int2bits-mone
Used simplifier rules:
list
/bitlista/
len-02
int-pot
/
pot2-pos
int-abs
/
leone
int-abs
/
sub-le-01
int-basic2
/
add-a
int-abs
/
minus-add
int-abs
/
lels-02
int-abs
/
anti
int-abs
/
mone-06
int-basic2
/
add-c
int-abs
/
lels-04
int-abs
/
zero-gels-04
nat-basic1
/
f
int-abs
/
forward-le-04
int-abs
/
forward-lele
int-abs
/
forward-lels
intnat
/
i2i-pos
int-abs
/
lels
int-abs
/
lels-03
int-basic1
/
ls-01
nat-basic1
/
one
int2bits
/
int2bits-not-empty
list-data
/bitlista/
l
nat-basic1
/
z
intnat
/
num-n2i-ls-02
int-basic1
/
forward-pos
int-abs
/
lels-01
int-abs
/
forward-le-05
int-abs
/
forward-le-01
int-abs
/
negle-13