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Proof step 1 from proof modmod-ma-negpos-neg (conclusion)

⊦ j0 + i0 * i < 0 ∧ j0 < 0 ∧ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → (j0 + i0 * i % j) % j = (j0 + i0 * i) % j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
j0 + i0 * i < j, j0 + i0 * i < 0, 0 < j, 0 ≤ i0, 0 ≤ i, j0 + 1 < j, j0 < j, j0 < 0, (j0 + i0 * i) + 1 < j ⊦ (j0 + i0 * i % j) % j = (j0 + i0 * i) % j

Rule argument

Additional information

Used simplifier rules: zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%succ-01: ⊦ i +1 = i + 1; from specification int-basic2%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%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%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs