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Theorem nummult-ls-02
⊦ 0 < i ∧ 0 ≤ j → ((* j) < (* i) * i0 ↔ j / i < i0)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
div-ls-mone
,
div-mult-two-nls-01
,
div-two-intro
,
div-twoodd-05
,
mod-zero-06
,
nummult-ls-02-01
,
Used by units in proved state:
int-pot
,
int-gcd
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 2
Proof steps: 5
Used lemmas:
div-elim-pospos
,
mult-ls
,
Used spec theorems:
int-mult
/
numls-02
Used simplifier rules:
int-abs
/
forward-le-05
int-abs
/
lels
int-abs
/
forward-le-01
int-abs
/
forward-lsle
int-abs
/
zero-gels-04
int-mult
/
zero-ge-add
int-abs
/
forward-lels
int-mult
/
zero-gr
int-abs
/
sub-ls-01
int-basic2
/
add-zero-rev
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
lenls
int-mult
/
associativity
int-mult
/
commutativity