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Theorem intshiftrsign32
⊦ # int2bits(i) ≤ 32 → i i>> j = bits2int(sublist(0, 32, mklist(int2bits(i).first, i→n(band(j, 31))) + fillsgn(32, int2bits(i))))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
intshiftrzero-prop-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 15
Proof steps: 35
Used lemmas:
band-max-02
,
band-ls-zero-01
,
band-associativity
,
band-commutativity
,
intshiftrsign
,
Used spec theorems:
list-del
/bitlista/
sublist-all
int2bits
/
bits2int-fill
bitopsaux
/
fill-fill
list-del
/bitlista/
sublist-append
list-del
/bitlista/
sublist-append-02
int2bits
/
bits2int-mklist-05
list-del
/bitlista/
sublist-mklist-01
int2bits
/
bits2int-mklist-06
Used simplifier rules:
nat
/
le-ls-simp
nat
/
lep-02
nat
/
ls-le-simp
nat-basic1
/
lf-01
nat
/
lep
intnat
/
num-i2n-ls
list-data
/bitlista/
l
nat
/
fle
int2bits
/
bits2int-mklist-02
list-del
/bitlista/
sublist-mklist-02
nat
/
let
nat-basic1
/
lf-02
nat-basic2
/
l-02
nat-basic2
/
eqs
nat-basic2
/
l-01
nat
/
lels-03
int2bits
/
bits2int-mklist-01
nat-basic1
/
ls-02
nat-basic1
/
f
nat
/
lels-01
int2bits
/
int2bits-not-empty
bitopsaux
/
fill-length
int2bits
/
int2int-inj
list-del
/bitlista/
sub-zero
list
/bitlista/
a
list
/bitlista/
Nil
list-last
/bitlista/
mk-zero
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
add-base
int-abs
/
forward-le-01
intnat
/
abs-zero
int-abs
/
numleledel
nat
/
elim-sub
list-last
/bitlista/
mk-len
int-abs
/
lels-01
intnat
/
num-i2n-le
int-abs
/
lels
int2bits
/
int2bits-first-02