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Theorem less-mult-div-01
⊦ 0 < i ∧ 0 < j ∧ 0 < j1 ∧ i1 < j → (i * i1) / j < i
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
div-sum-ls
,
less-mult-div-02
,
nls-mult-div
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 15
Used lemmas:
div-zero-05
,
div-elim-negpos
,
div-elim
,
Used spec theorems:
int-basic2
/
ex-ls-add
int-abs
/
ex-le-add
int-mult
/
dist-lsplit
int-basic2
/
zero-06
Used simplifier rules:
int-abs
/
forward-le
int-abs
/
forward-le-04
int-abs
/
lels-03
int-abs
/
anti
int-mult
/
zero-left
int-basic1
/
forward-pos
int-abs
/
forward-lels
int-basic2
/
zero-02
int-abs
/
forward-le-05
int-basic2
/
eq
int-basic1
/
lf-01
int-basic1
/
trans
int-basic1
/
lf-02
int-abs
/
forward-lsle
int-abs
/
forward-le-02
int-basic2
/
succ-01
int-mult
/
ls-dist-02
int-basic2
/
ls-01
int-basic2
/
ls-02
int-mult
/
zero-gr
int-abs
/
zero-gels-01
int-basic2
/
ls
int-basic2
/
add-c
int-basic2
/
add-a
int-basic2
/
add-zero-rev
int-abs
/
forward-le-01
int-abs
/
lels
int-mult
/
zero-neq-01
int-mult
/
associativity
int-mult
/
commutativity
int-mult
/
zero-ls
int-basic1
/
ls-01
int-abs
/
lenls