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Theorem modeq-neg-02
i0 * j + j0 < 0, 0 < j, 0 ≤ j0, j0 % j ≠ 0 ⊦ (i0 * j + j0) % j = j0 % j - 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: 8
Proof steps: 14
Used lemmas:
div-elim2
,
div-elim-pos
,
Used spec theorems:
int-mult
/
modeqp-copied
int-basic2
/
ls
Used simplifier rules:
int-mult
/
zero-ls
int-abs
/
forward-le-01
int-mult
/
dist-rmerge
int-abs
/
zero-gels-04
int-abs
/
forward-lele
int-abs
/
forward-le-04
int-basic2
/
eq
int-basic2
/
ls-01
int-mult
/
ls-pos
int-basic2
/
ls
int-abs
/
abs-16
int-abs
/
lenls
int-abs
/
forward-lels
int-abs
/
lels
int-abs
/
lels-01
int-abs
/
sub-ls
int-abs
/
sub-le-01
int-mult
/
eq-succ-01
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
succ-rmerge
int-abs
/
sub-eq
int-abs
/
sub-add-01
int-abs
/
sub-sub
int-basic2
/
add-zero
int-abs
/
zero-gels-01
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-abs
/
forward-le-05
int-basic1
/
forward-pos
int-abs
/
neg-13
int-abs
/
abs-08
int-abs
/
lels-02
int-mult
/
add-mult-two
int-basic2
/
add-a
int-basic2
/
add-c
int-basic2
/
add-in
int-basic1
/
ls-01