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Proof step 9 from proof modmod-add-zero (previous step)

i0 < 0, (i + i0 % j) % j = 0, 0 < j ⊦ (i + i0) % j = 0, 0 = j, 0 ≤ i0 ∧ 0 ≤ i, i ≤ 0 ∧ i0 ≤ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
(i + i0 % j) % j = 0, i0 < 0, 0 < j ⊦ 0 = j, (i + i0) % j = 0, 0 ≤ i0, i ≤ 0 ∧ i0 ≤ 0

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs