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Theorem div-inshort
⊦ s2i(sho1) ≠ 0 → ((s2i(sho0) / s2i(sho1))∈short ↔ ¬(s2i(sho1) = ~1 ∧ s2i(sho0) = ~32768))
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: 24
Proof steps: 42
Used lemmas:
short-min-03
,
inshort-le-num
,
short-ls
,
short-ngr
,
short-max-06
,
short-min-01
,
inshort
,
Used spec theorems:
int-div
/
abs-intro
int-div
/
Div-left
int-div
/
Div-right
int-div
/
div-nls
int-div
/
div-zero-ngr
int-div
/
div-rec-01
int-div
/
div-nls-01
int-abs
/
Abs-neg
int-abs
/
ls-rew-succ
Used simplifier rules:
int-abs
/
forward-le-04
int-abs
/
negle-13
int-abs
/
minus-add
int-div
/
div-mone-01
int-div
/
div-zero-ngr-01
int-abs
/
numle-03
int-abs
/
sub-le-01
int-abs
/
Abs-pos
int-abs
/
sub-ls
int-abs
/
numlelsdel-01
int-abs
/
neg-06
int-abs
/
minus-sub
int-abs
/
minus-neg
int-abs
/
numle-02
int-abs
/
mone-08
int-abs
/
abs-03
int-abs
/
sub-eq
int-abs
/
abs-06
int-abs
/
numleledel-01
int-abs
/
sub-le
int-abs
/
mone-06
int-abs
/
numls-02
int-abs
/
abs-08
int-basic1
/
numlslsdel-01
int-basic1
/
forward-pos
int-div
/
div-zero-nls-01
int-div
/
neg
int-abs
/
lels-04
int-abs
/
neg
int-abs
/
forward-lsle
int-abs
/
forward-le-01
int-abs
/
zero-gels-01
int-basic1
/
lst-01
int-div
/
neg-01
int-abs
/
numlelsdel
int-abs
/
negle-07
int-basic2
/
add-zero
int-abs
/
neg-07
int-abs
/
numls-03
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
forward-le-05
int-abs
/
forward-le-02
int-abs
/
lels-03
int-basic1
/
ls-01
int-abs
/
lels-02
int-abs
/
lels
int-basic1
/
numlsf
int-abs
/
lels-01