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Theorem div-ls-same
⊦ 0 < j → (i < i / j ↔ i < 0 ∧ 1 < j)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
div-nle
,
div-nls
,
div-zero-ngr
,
div2-notzero
,
le-abs-numerator
,
ls
,
Used by units in proved state:
int-gcd
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 17
Used lemmas:
div-elim-pospos
,
div-elim-negpos
,
Used spec theorems:
int-abs
/
lels-04
int-abs
/
lels
int-abs
/
ple-04
int-mult
/
ls-same-06
Used simplifier rules:
int-basic2
/
lst-03
int-abs
/
forward-le-04
int-mult
/
one-01
int-abs
/
abs-08
int-abs
/
neg-13
int-basic1
/
lf-02
int-abs
/
numls-02
int-abs
/
mone-06
int-mult
/
modzero-02
int-abs
/
zero-gels-03
int-basic1
/
forward-pos
int-basic2
/
add-zero-rev
int-mult
/
le-same-03
int-abs
/
bet
int-abs
/
forward-lels
int-abs
/
lels
int-abs
/
forward-le-01
int-abs
/
forward-le-05
int-abs
/
zero-gels-04
int-mult
/
zero-ge-add
int-basic1
/
lf-01
int-basic1
/
trans
int-abs
/
forward-lsle
int-abs
/
forward-le-02
int-basic2
/
succ-01
int-abs
/
zero-gels-01
int-basic2
/
ls
int-mult
/
zero-ls
int-abs
/
sub-ls
int-basic2
/
add-a
int-abs
/
lsone
int-abs
/
lels-03
int-mult
/
associativity
int-mult
/
commutativity
int-basic2
/
add-c