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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: s, ls,
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: 18
Proof steps: 27
Used lemmas:
zero
,
prod-div-less-01
,
prod-div-less
,
div-mult-03
,
div-zero-ngr
,
mod-mult-04
,
div-add-pos
,
Used spec theorems:
int-mult
/
exdivmodpos
int-mult
/
dist-lsplit
int-mult
/
associativity
int-mult
/
commutativity
int-basic2
/
add-c
int-abs
/
le-def
int-abs
/
forward-lels
Used simplifier rules:
int-abs
/
forward-le-05
int-abs
/
forward-le
int-abs
/
lels
int-abs
/
forward-le-01
int-basic1
/
ls-01
int-abs
/
le-def
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
zero-ge-02
int-mult
/
zero-ge
int-basic2
/
add-c
int-basic2
/
add-a
int-mult
/
dist-rmerge
int-abs
/
zero-gels-01
int-basic1
/
forward-pos
int-abs
/
forward-lsle
int-abs
/
forward-le-02
int-abs
/
lels-02
int-mult
/
zero-ls
int-mult
/
zero-ge-add
int-abs
/
lels-03
int-basic2
/
add-zero
int-mult
/
Mult-zero
int-abs
/
zero-gels-03
int-mult
/
zero-ge-01
int-abs
/
zero-gels-04
int-mult
/
zero-gr
int-mult
/
le-pos
int-basic2
/
ls-01
int-mult
/
ls-forward
int-mult
/
ls-pos