[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 div-add1-negpos-neg-02
⊦ i % j = 0 ∧ i + i0 < 0 ∧ i < 0 ∧ 0 ≤ i0 ∧ 0 < j → (i + i0) / j = i / j + (i0 + (j - 1)) / j
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 2
Proof steps: 2
Used lemmas:
div-add1-negpos-neg
,
mod-zero-04
,
div-zero-05
,
div-add1-negpos-neg-01
,
one
,
mod-one
,
mod-ls-same-02
,
div-add-succ
,
div-add-nosucc
,
Used spec theorems:
Used simplifier rules:
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
numadd
int-basic2
/
add-zero-rev
int-basic2
/
add-in
int-abs
/
sub-add-01
int-abs
/
zero-gels-04
int-abs
/
forward-le-05
int-abs
/
forward-le-01
int-basic1
/
lf-01
int-basic1
/
trans
int-basic1
/
lf-02
int-abs
/
forward-lsle
int-abs
/
forward-le-02
int-basic2
/
succ-01
int-abs
/
zero-gels-01
int-abs
/
numls-03
int-basic2
/
ls
int-abs
/
abs-16
int-abs
/
abs-08
int-abs
/
negle-07
int-abs
/
numsub
int-basic1
/
lst-01
int-abs
/
lsone
int-abs
/
lels-03
int-abs
/
numlelsdel-01
int-abs
/
lels
int-abs
/
anti
int-basic1
/
forward-pos
int-abs
/
forward-lels
int-abs
/
forward-le-04
int-abs
/
forward-lele