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Theorem le-abs-numerator
j ≠ 0 ⊦ ~ abs(i) ≤ i / j ∧ i / j ≤ abs(i)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 15
Proof steps: 27
Used lemmas:
div-elim-posneg
,
div-zero-ngr-01
,
div-ls-zero
,
Div-left
,
div-elim-negneg
,
zero-05
,
div-ls-same
,
div-zero-nls
,
ls-same-pos
,
Used spec theorems:
int-abs
/
zero-gs
int-mult
/
dist-lsplit
Used simplifier rules:
int-abs
/
negle-13
int-abs
/
negle-07
int-basic2
/
add-zero
int-abs
/
sub-le-01
int-abs
/
neg-15
int-abs
/
forward-lele
int-basic2
/
ls-02
int-mult
/
zero-gr-02
int-mult
/
one
int-abs
/
lels-03
int-basic1
/
lst-01
int-abs
/
neg-02
int-abs
/
abs-06
int-abs
/
neg-05
int-abs
/
neg
int-abs
/
neg-11
int-abs
/
abs-03
int-abs
/
forward-lels
int-abs
/
forward-le-04
int-abs
/
absls
int-abs
/
forward-le-05
int-abs
/
lels-01
int-abs
/
absle
int-abs
/
lenls
int-abs
/
lels
int-abs
/
zero-gels-04
int-mult
/
modzero-05
int-abs
/
lsone
int-mult
/
ls-same-03
int-basic2
/
ls-01
int-abs
/
zero-gels-01
int-abs
/
forward-le-01
int-abs
/
zero-gels-03
int-abs
/
neg-07
int-abs
/
abs-08
int-abs
/
forward-lsle
int-abs
/
forward-le-02
int-basic2
/
ls
int-mult
/
zero-ls-01
int-abs
/
numls-02
int-abs
/
mone-06
int-abs
/
lels-02
int-basic1
/
ls-01
int-basic2
/
add-a
int-basic2
/
add-c
int-mult
/
associativity
int-mult
/
commutativity