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Proof step 2 from proof noeth-modlep (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 3:
abs(j) < j2 +1, j0 < abs(j), 0 ≤ j0, abs(j) * i ≤ abs(j) * i0 + j0, ∀ j0, j, i, i0. j0 < abs(j) ∧ abs(j) < j2 ∧ abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 → i ≤ i0 ⊦ i ≤ i0
Proof step 35:
abs(j) < j2 -1, j0 < abs(j), 0 ≤ j0, abs(j) * i ≤ abs(j) * i0 + j0, ∀ j0, j, i, i0. j0 < abs(j) ∧ abs(j) < j2 ∧ abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 → i ≤ i0 ⊦ i ≤ i0

Rule argument

indvar: j1

Additional information

Used simplifier rules: int generated by 0, +1, -1;;% ⊦ i < 0 ∧ 0 ≤ j → ¬ j < i; (s)