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Proof step 13 from proof div-ls-zero (previous step)

0 < j * (i0 + 1) + j0, 0 < j + j0, j0 < 0, 0 < j, i0 < j, j0 < j, i0 * j + j0 < 0, i0 < 0, i0 ≤ 0 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
j0 < j, i0 < j, 0 < j, j0 < 0, 0 < j + j0, i0 < 0, 0 < j * (i0 + 1) + j0 ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (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% ⊦ i < 0 ∧ j0 < j ∧ 0 < j → i * j + j0 < 0; (s)% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; (s)