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

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

Rule argument

Additional information

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