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Theorem div-eq-zero-01
⊦ 0 ≠ j → (i / j = 0 ↔ abs(i) < abs(j))
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
div-abs
,
div-minus-onediff-01
,
div-zero-02
,
mod-div-zero
,
Used by units in proved state:
int-gcd
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 29
Used lemmas:
div-elim-posneg
,
div-elim-pospos
,
zero
,
div-same
,
div-elim-negneg
,
div-elim-negpos
,
div-eq-zero
,
Used spec theorems:
int-mult
/
numle-12
Used simplifier rules:
int-abs
/
abs-16
int-abs
/
forward-le-02
int-basic1
/
ls-01
int-abs
/
neg-13
int-abs
/
abs-08
int-abs
/
lels
int-abs
/
forward-lels
int-abs
/
neg-15
int-abs
/
sub-le
int-basic2
/
add-zero
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
anti
int-abs
/
zero-gels-03
int-mult
/
Mult-zero
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
zero-gels-01
int-basic1
/
lst-01
int-abs
/
forward-le-05
int-mult
/
succ-rmerge
int-abs
/
forward-le-04
int-basic2
/
ls-02
int-mult
/
zero-gr
int-abs
/
numls-02
int-abs
/
mone-06
int-abs
/
lels-02
int-abs
/
sub-ls-01
int-mult
/
modzero-02
int-abs
/
numadd-01
int-mult
/
ls-dist-04
int-abs
/
succ-02
int-abs
/
zero-gels-04
int-mult
/
zero-gr-add-01
int-abs
/
elim-sub
int-abs
/
forward-le-01
int-abs
/
Abs-pos
int-abs
/
abs-06
int-abs
/
forward-lsle
int-abs
/
neg-07
int-abs
/
zero-gels
int-abs
/
lels-03
int-basic2
/
ls
int-mult
/
zero-ls-01