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Proof step 1 from proof modmod-add2-posneg-neg-02 (conclusion)

⊦ 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

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: modmod-add-zero: 0 < j ⊦ (i + i0 % j) % j = 0 → (i + i0) % j = 0;%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2