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Theorem modeq-pos-03
0 ≤ i0 * j + j0, 0 < j, j0 < 0, j0 % j ≠ 0 ⊦ (i0 * j + j0) % j = j0 % j + j
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
modeq-pos-04
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 2
Proof steps: 5
Used lemmas:
modeq-pos-01
,
div-elim2
,
Used spec theorems:
int-mult
/
commutativity
Used simplifier rules:
int-abs
/
numlsf-01
int-abs
/
forward-lele
int-abs
/
forward-lels
int-mult
/
ls-pos
int-abs
/
lsone
int-mult
/
ls-same
int-mult
/
ls-add
int-mult
/
zero-gr
int-basic2
/
ls-02
int-basic2
/
ls-01
int-basic2
/
succ-01
int-abs
/
forward-lsle
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
lels-02
int-basic2
/
add-a
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
dist-rmerge
int-basic2
/
add-c
int-abs
/
abs-08
int-abs
/
neg-13