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Proof step 1 from proof noeth-modlep (conclusion)

⊦ abs(j) < j1 → abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 ∧ j0 < abs(j) → i ≤ i0

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ j, i, i0, j0. abs(j) < j2 → abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 ∧ j0 < abs(j) → i ≤ i0 ⊦ abs(j) < j2 +1 → abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 ∧ j0 < abs(j) → i ≤ i0
Proof step 34:
∀ j, i, i0, j0. abs(j) < j2 → abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 ∧ j0 < abs(j) → i ≤ i0 ⊦ abs(j) < j2 -1 → abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 ∧ j0 < abs(j) → i ≤ i0

Rule argument

indvar: j1

Additional information

Used simplifier rules: int generated by 0, +1, -1;;%zero-gels: ⊦ i < 0 ∧ 0 ≤ j → ¬ j < i; from specification int-abs