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Theorem nummult-le-03
⊦ 0 < i ∧ j < 0 → ((* j) ≤ (* i) * i0 ↔ j / i ≤ i0)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
div2-add-neg
,
nummult-le-03-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 3
Proof steps: 9
Used lemmas:
div-elim2
,
Used spec theorems:
int-mult
/
modlep-02
int-mult
/
modlsp-01
Used simplifier rules:
int-abs
/
forward-le-05
int-abs
/
forward-le-04
int-abs
/
lels-03
int-mult
/
modzero-02
int-abs
/
forward-lels
int-abs
/
forward-le-02
int-abs
/
zero-gels-03
int-abs
/
lsone
int-mult
/
ls-same
int-mult
/
associativity
int-mult
/
zero-ls
int-basic2
/
lst-04
int-abs
/
numls-03
int-basic2
/
succ-01
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
lels-01
int-abs
/
anti
int-basic2
/
add-a
int-basic2
/
add-c
int-basic2
/
lst-03
int-abs
/
zero-gels-01
int-abs
/
ler
int-mult
/
commutativity
int-basic2
/
ls-02
int-abs
/
lenls