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Proof step 1 from proof mod-add-neg (conclusion)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
i0 % j = 0, i < j, 0 < j, i < 0, i0 + 1 < j, i0 < j, i0 < 0, i + 1 < j ⊦ (i + i0) % j = i % j

Rule argument

Additional information

Used simplifier rules: mod-less-01: ⊦ 0 < j → i % j < j;%succ-01: ⊦ i +1 = i + 1; from specification int-basic2%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%lf-03: ⊦ i < j ∧ i = i0 → i0 < j; (forward) from specification int-basic1