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Theorem div-sum-ls
⊦ 0 ≤ i ∧ 0 ≤ i1 ∧ 0 < i + i1 ∧ 0 < j1 ∧ 0 < j2 ∧ 0 < j ∧ j1 < j ∧ j2 < j → (i * j1 + i1 * j2) / j < i + i1
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
div-sum-ls-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 11
Used lemmas:
ls-02
,
less-mult-div-01
,
Used spec theorems:
int-mult
/
dist-lsplit
int-abs
/
le-def
int-mult
/
dist-rsplit
int-basic2
/
add-c
int-basic2
/
nls
Used simplifier rules:
int-abs
/
forward-le-01
int-abs
/
forward-le-05
int-basic1
/
forward-pos
int-abs
/
forward-le
int-abs
/
forward-lele
int-abs
/
forward-lsle
int-abs
/
lels
int-abs
/
lels-04
int-basic1
/
irref
int-abs
/
lels-01
int-mult
/
dist-rmerge
int-mult
/
associativity
int-mult
/
commutativity
int-basic2
/
add-a
int-basic2
/
add-c
int-mult
/
ls-forward
int-abs
/
lels-02
int-mult
/
ls-pos
int-abs
/
sub-ls
int-abs
/
succ-02
int-abs
/
lels-03