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Theorem div-nearer-zero
j ≠ 0 ⊦ abs(i / j * 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: 13
Proof steps: 20
Used lemmas:
div-lezero
,
neg-01
,
Div-right
,
ls-same-pos-02
,
abs
,
Used spec theorems:
int-abs
/
Abs-neg
Used simplifier rules:
int-abs
/
lels-01
int-mult
/
abs-eqall
int-abs
/
forward-le-01
int-abs
/
Abs-pos
int-mult
/
zero-gr
int-abs
/
forward-lels
int-abs
/
forward-lsle
int-mult
/
zero-gr-01
int-abs
/
zero-gels-04
int-abs
/
abs-07
int-abs
/
abs-16
int-basic1
/
lst-01
int-abs
/
neg-05
int-mult
/
zero-left
int-basic1
/
ls-01
int-abs
/
lsone
int-mult
/
ls-same
int-basic2
/
lst-04
int-abs
/
numlelsdel
int-abs
/
numls-03
int-basic2
/
succ-01
int-mult
/
zero-ls
int-abs
/
forward-le-02
int-abs
/
forward-le-05
int-basic1
/
trans
int-basic1
/
lf-01
int-basic1
/
numlsf
int-mult
/
zero-ls-01
int-abs
/
neg-06
int-abs
/
lels
int-abs
/
lels-03
int-abs
/
neg-12
int-abs
/
neg-10
int-abs
/
neg-02
int-mult
/
minus-left
int-mult
/
associativity
int-abs
/
neg-01
int-abs
/
negle-07
int-basic2
/
add-zero-rev
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
zero-gels-03
int-abs
/
neg
int-abs
/
zero-gels-01
int-mult
/
commutativity