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Proof step 6 from proof pnls-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
i0 * j0 < i * j, i ≤ i0, j ≤ j0, 0 ≤ i0, 0 ≤ i, 0 ≤ j0, 0 ≤ j ⊦ 0 < i ∧ 0 < j

Rule argument

Additional information

Used simplifier rules: forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs% ⊦ i ≤ j ↔ ¬ j < i; (ss)