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Proof step 17 from proof modmod-add-zero (previous step)

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

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs