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

¬(i + i0 < 0 ∧ i < 0 ∧ 0 ≤ i0 ∧ 0 < j), i < j, i < 0, 0 < j, i + 1 < j ⊦ (i + i0) % j = (i + i0 % j) % j + j, (i + i0 % j) % j = (i + i0) % j + j, (i + i0 % j) % j = (i + i0) % j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
i < j, i < 0, 0 < j, i + 1 < j ⊦ (i + i0) % j = (i + i0 % j) % j + j, (i + i0 % j) % j = (i + i0) % j + j, (i + i0 % j) % j = (i + i0) % j, i + i0 < 0 ∧ 0 ≤ i0

Rule argument

Additional information

Used simplifier rules: zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs