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Theorem prod-div-less
⊦ 0 < i ∧ i < j ∧ 0 < i1 ∧ i1 < j → (i * i1) / j < i
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
prod-div-less-01
,
quad-div-less
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 10
Used lemmas:
div-elim-pospos
,
Used spec theorems:
int-mult
/
modneqp
int-basic2
/
add-zero
Used simplifier rules:
int-basic1
/
trans
int-basic1
/
lf-01
int-basic1
/
forward-pos
int-abs
/
forward-le
int-abs
/
forward-le-05
int-abs
/
forward-le-01
int-mult
/
zero-ge
int-abs
/
lels-01
int-basic1
/
ls-01
int-abs
/
ler
int-abs
/
anti
int-mult
/
ls-pos
int-abs
/
lels
int-abs
/
lels-03
int-basic2
/
add-c
int-basic2
/
add-a
int-mult
/
commutativity
int-mult
/
associativity
int-basic1
/
irref
int-mult
/
mods-ls-04