[Imprint]
[Data Privacy Statement]
[E-Mail]
View
long theorem info
. View
the proof
. Back to
main index
. View
the specification
. View
theorem base summary
, View
theorem base listing
, the
used properties by spec
, the
dependency list
, the
symbol table
,
Theorem mod-ls-same-01
j ≠ 0 ⊦ i % j < i ↔ 0 < i ∧ (abs(j) = 1 ∨ abs(j) ≤ i)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
mod-nls-02
,
mod-zero-06
,
mod-zero-ls
,
modmod-add-case
,
modmod-add-if
,
modmod-add2-negpos-pos-01
,
Used by units in proved state:
int-pot
,
intnat
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 21
Used lemmas:
div-elim-posneg
,
div-elim-pospos
,
modnum-neg-01
,
mod-one
,
mod-zero-04
,
div-elim-negneg
,
div-elim-negpos
,
Used spec theorems:
int-abs
/
Abs-neg
int-abs
/
le-def
Used simplifier rules:
int-abs
/
neg-13
int-abs
/
forward-le
int-abs
/
neg-06
int-abs
/
Abs-pos
int-abs
/
abs-16
int-mult
/
zero-gr
int-mult
/
ls-add
int-abs
/
lenls
int-basic1
/
ls-01
int-abs
/
numadd-01
int-abs
/
negeq
int-basic1
/
lst-01
int-basic2
/
lst-03
int-abs
/
lsone
int-abs
/
forward-le-04
int-abs
/
forward-lels
int-abs
/
forward-le-05
int-abs
/
lels-02
int-abs
/
neg-07
int-abs
/
abs-08
int-abs
/
lels
int-abs
/
forward-le-01
int-abs
/
forward-lele
int-abs
/
forward-lsle
int-abs
/
zero-gels-04
int-abs
/
zero-gels-01
int-basic2
/
ls-01
int-mult
/
ls-same-03
int-abs
/
numls-03
int-basic2
/
add-a
int-basic2
/
add-c
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
zero-gels-03
int-basic1
/
lf-01
int-abs
/
forward-le-02
int-basic1
/
trans
int-basic2
/
succ-01
int-basic2
/
ls
int-mult
/
ls-add-03
int-mult
/
one
int-basic1
/
irref
int-mult
/
ls-add-02
int-mult
/
zero-ls-01
int-abs
/
numls-02
int-abs
/
mone-06
int-abs
/
lels-03
int-abs
/
anti
int-basic1
/
lf-02
int-basic2
/
ls-02
int-mult
/
zero-gr-01