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Proof step 5 from proof pnle-pos (previous step)

¬(0 < i ∧ 0 < j ∧ i ≤ i0 ∧ j < j0), i ≤ i0, j < j0, i0 ≠ 0, 0 ≤ i, 0 ≤ j ⊦ i * j < i0 * j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
i0 * j0 ≤ i * j, j < j0, i ≤ i0, 0 < j0, 0 ≤ j, 0 ≤ i, 0 < i0 ⊦ i0 = 0, 0 < i ∧ 0 < j

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%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%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs