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Theorem div-add-neg
⊦ i0 % j = 0 ∧ i < 0 ∧ i0 < 0 ∧ 0 < j → (i + i0) / j = i / j + i0 / j
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
div-add1-negneg
,
Used by units in proved state:
int-pot
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 2
Proof steps: 7
Used lemmas:
diveq-neg
,
div-elim2
,
mod-less-01
,
Used spec theorems:
int-mult
/
commutativity
Used simplifier rules:
int-basic1
/
lf-03
int-abs
/
forward-lels
int-basic1
/
lf-02
int-basic2
/
succ-01
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
lsone
int-mult
/
ls-same
int-mult
/
zero-ls
int-basic2
/
add-zero
int-mult
/
dist-rmerge
int-abs
/
lels
int-abs
/
forward-lsle
int-abs
/
forward-lele
int-basic2
/
ls-01
int-mult
/
ls-pos
int-basic2
/
ls-02
int-basic1
/
ls-01
int-basic2
/
add-a
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
lep
int-mult
/
modzero
int-basic2
/
add-c