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Proof step 4 from proof modeq-neg (previous step)

j0 = i1 * j + j1 ∧ j1 ≤ 0 ∧ abs(j1) < j, i0 * j + j0 < 0, 0 < j, j0 < 0 ⊦ (i0 * j + j0) % j = j1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
0 < j, abs(j1) < j, i1 * j + j1 < 0, j1 ≤ 0, j1 < j, j * (i1 + i0) + j1 < 0 ⊦ (j * (i1 + i0) + j1) % j = j1

Rule argument

Additional information

Used simplifier rules: forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) 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%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%dist-rmerge: ⊦ i * j + i * j0 = i * (j + j0); from specification int-mult