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Theorem div-ngr-zero
⊦ i < 0 ∧ 0 < j → (0 ≤ i / j ↔ abs(i) < j)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
letwozero
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 1
Proof steps: 4
Used lemmas:
div-elim-negpos
,
Used spec theorems:
Used simplifier rules:
int-abs
/
zero-gels-01
int-basic2
/
lst-03
int-abs
/
forward-le-04
int-abs
/
anti
int-abs
/
lels-02
int-mult
/
modzero-02
int-mult
/
associativity
int-mult
/
commutativity
int-basic2
/
add-a
int-basic2
/
add-c
int-basic1
/
lf-01
int-basic1
/
trans
int-abs
/
forward-le-02
int-abs
/
forward-le-05
int-abs
/
forward-lels
int-basic2
/
succ-01
int-basic2
/
ls-02
int-mult
/
zero-gr-add
int-abs
/
lels-03
int-mult
/
zero-left
int-basic2
/
add-zero-rev
int-abs
/
numlslsdel-03
int-abs
/
zero-gels-03
int-abs
/
abs-08
int-abs
/
neg-13
int-abs
/
lels