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Theorem div-elim-posneg
⊦ j < 0 ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < abs(j) ∧ i0 ≤ 0)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
div-eq-same
,
div-eq-zero-01
,
div-zero-ngr-01
,
le-abs-numerator
,
mod-div-zero
,
mod-ls-same-01
,
mod-ls-same-02
,
mod-neq
,
mod-zero-06
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 1
Proof steps: 4
Used lemmas:
div-elim1
,
Used spec theorems:
int-mult
/
modeqp-02
Used simplifier rules:
int-abs
/
forward-lele
int-abs
/
forward-le-04
int-mult
/
commutativity
int-mult
/
associativity
int-abs
/
lsone
int-mult
/
ls-same-03
int-basic2
/
ls-01
int-basic2
/
add-c
int-basic2
/
add-a
int-basic2
/
ls
int-abs
/
forward-le-01
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-abs
/
zero-gels-04
int-abs
/
zero-gels-01
int-abs
/
abs-08
int-abs
/
neg-07