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Theorem modmod-add2-posneg-neg-01
⊦ 0 ≤ i + i0 % j ∧ i + i0 < 0 ∧ 0 ≤ i ∧ i0 < 0 ∧ (i + i0 % j) % j ≠ 0 ∧ 0 < j → (i + i0 % j) % j = (i + i0) % j + j
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
modmod-add-case
,
modmod-add-if
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 4
Proof steps: 6
Used lemmas:
mod-mult-04
,
mod-add1-negpos-neg
,
div-elim-negpos
,
mod-one
,
mod-ls-same-02
,
Used spec theorems:
Used simplifier rules:
int-abs
/
negle-07
int-abs
/
abs-08
int-abs
/
abs-16
int-abs
/
forward-le-05
int-abs
/
zero-gels-03
int-abs
/
lep-02
int-mult
/
modzero-02
int-basic2
/
ls
int-basic2
/
ls-01
int-basic2
/
lst-03
int-basic2
/
succ-01
int-abs
/
forward-lele
int-abs
/
forward-le-04
int-abs
/
forward-lels
int-abs
/
forward-le-01
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
Sub-def
int-basic2
/
add-a
int-basic2
/
add-c
int-mult
/
zero-left
int-mult
/
associativity
int-mult
/
commutativity
int-basic2
/
add-zero-rev
int-abs
/
zero-gels-01
int-mult
/
zero-ls
int-abs
/
zero-gels-04