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Theorem div-add1-posneg-pos-02
⊦ i % j = 0 ∧ 0 ≤ i + i0 ∧ 0 ≤ i ∧ i0 < 0 ∧ 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: 3
Proof steps: 5
Used lemmas:
div-add1-posneg-pos-01
,
div-add1-negpos-pos
,
one
,
one-01
,
div-add-succ-neg
,
div-add-nosucc-neg
,
Used spec theorems:
Used simplifier rules:
int-abs
/
sub-add-01
int-abs
/
sub-eq
int-abs
/
Sub-def
int-basic2
/
succ-01
int-abs
/
forward-le-01
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
forward-le-05
int-abs
/
zero-gels-01
int-abs
/
sub-sub-04
int-abs
/
elim-sub
int-basic2
/
add-a
int-basic2
/
add-c
int-basic2
/
add-in
int-abs
/
lels
int-abs
/
bet
int-basic1
/
lf-02
int-abs
/
numadd
int-basic2
/
add-zero-rev