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Theorem nummult-ls
⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 < (* j) ↔ i0 < (i + j - 1) / i)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
div-div-pred
,
div-div-pred-01
,
div-mult-three
,
div-two-intro
,
div-twoodd-03
,
div2-nls-02
,
even-not-ex
,
mod-two-pred-01
,
nummult-ls-04
,
Used by units in proved state:
int-pot
,
int-square
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 19
Used lemmas:
div-elim-pos
,
Used spec theorems:
int-mult
/
modlep
Used simplifier rules:
int-abs
/
forward-le-04
int-basic2
/
ls
int-abs
/
forward-lele
int-abs
/
lels-03
int-mult
/
eq-succ
int-abs
/
lels
int-mult
/
zero-ge-add
int-abs
/
forward-le-05
int-basic1
/
lf-02
int-abs
/
leone
int-abs
/
sub-le-01
int-abs
/
sub-eq
int-abs
/
zero-gels-04
int-mult
/
zero-ge
int-abs
/
forward-le-01
int-abs
/
forward-lels
int-abs
/
succ-01
int-basic2
/
add-in
int-basic2
/
add-zero-rev
int-abs
/
numadd
int-mult
/
eq-dist
int-mult
/
one
int-mult
/
associativity
int-mult
/
commutativity
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
succ-02
int-abs
/
numls-02
int-abs
/
mone-06
int-abs
/
numle-02
int-abs
/
numleledel-01
int-mult
/
mods-ls-04
int-abs
/
lenls
int-abs
/
elim-sub