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Proof step 1 from proof modzero-02 (conclusion)

⊦ i < 0 ∧ j0 < j ∧ 0 < j → i * j + j0 < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
i < j, i < i * j + j0, 0 ≤ i * j + j0, 0 < j, j0 < j, i < 0, i + 1 < j ⊦

Rule argument

Additional information

Used simplifier rules: succ-01: ⊦ i +1 = i + 1; from specification int-basic2%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%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs