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Theorem nummult-le-01
⊦ 0 < i ∧ j < 0 → ((* i) * i0 ≤ (* j) ↔ i0 ≤ (j + 1 - i) / i)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
div-div-pred-01
,
exeven
,
ls-even-01
,
modeven-neg
,
nummult-le-01-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 14
Used lemmas:
div-elim2
,
div-elim-pos
,
Used spec theorems:
int-abs
/
le-def
int-mult
/
modlsp-01
int-mult
/
modlep-02
Used simplifier rules:
int-abs
/
lels-03
int-abs
/
forward-lels
int-basic2
/
add-zero
int-mult
/
succ-rmerge
int-abs
/
sub-eq
int-abs
/
lsone
int-abs
/
lels-02
int-abs
/
sub-ls
int-abs
/
sub-le-01
int-basic2
/
add-in
int-abs
/
Sub-def
int-basic2
/
lst-04
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
zero-ls
int-basic2
/
succ-01
int-abs
/
forward-lsle
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
les
int-basic1
/
lf-03
int-basic1
/
lf-02
int-abs
/
numls-03
int-abs
/
succ-02
int-abs
/
ler
int-basic2
/
lst-03
int-basic2
/
ls-02
int-abs
/
lels
int-abs
/
succ-01
int-abs
/
lels-04
int-basic2
/
add-a
int-basic2
/
add-c