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Theorem modmod-add-02
0 ≠ j ⊦ i ≤ 0 ∧ i0 ≤ 0 → (i % j + i0) % j = (i + i0) % j
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
modmod-add-03
,
modmod-add-case
,
modmod-add-if
,
modmod-add-zero
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 1
Proof steps: 2
Used lemmas:
mod-neg-01
,
modmod-add-01
,
Used spec theorems:
Used simplifier rules:
int-abs
/
forward-le-04
int-abs
/
negle-07
int-basic2
/
add-zero-rev
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
zero-gels-04
int-abs
/
neg-11
int-abs
/
neg-12