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Proof step 1 from proof pls-pos (conclusion)

0 < i, 0 < j, i ≤ i0, j < j0 ⊦ i * j < i0 * j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
i ≤ i0, j < j0, i0 * j0 ≤ i * j, 0 < i, 0 < j, 0 < j0, 1 < j0, 0 < i0 ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (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: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs