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Theorem cast-band
n→i((# int2bits(j0))-1) ≤ i, 0 ≤ j0 ⊦ band(cast(i, j), j0) = band(j, j0)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
cast-law-shift-snd-l
,
cast-law-shift-snd-r
,
cast-law-shift-snd-zr
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 16
Used lemmas:
bitsand-cast-05
,
and-bits2int-sgn
,
and-rec-02
,
band-def
,
cast-def
,
Used spec theorems:
int2bits
/
bits2bits-def
int2bits
/
bits2int-sgn-intro
Used simplifier rules:
int2bits
/
bits2int-sgn
nat-basic1
/
one-01
nat
/
lels-01
nat
/
ls-03
nat-basic2
/
a
nat-basic2
/
c
int2bits
/
int2bits-first-02
int-abs
/
lels-04
nat-basic1
/
lf-01
nat-basic1
/
f
nat-basic2
/
oz
nat-basic2
/
l
intnat
/
inni-ls
int2bits
/
bits2int-zero
int2bits
/
int2bits-zero
int2bits
/
int2bits-len-one
intnat
/
nat2int-10
list-del
/bitlista/
lastN-zero
bitopsaux
/
fill-zero
intnat
/
abs-zero
list-del
/bitlista/
lastN-empty
int-abs
/
forward-le-01
nat
/
pred-03
list-data
/bitlista/
l
int2bits
/
int2bits-not-empty
nat
/
elim-pred-c