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Proof step 3 from proof noeth-modlep (previous step)

j0 < j2, 0 ≤ j0, i0 < i, abs(j) ≤ j2, j0 < abs(j), abs(j) * i ≤ abs(j) * i0 + j0, 0 < j2, ∀ j, i, i0, j0. abs(j) < j2 → abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 ∧ j0 < abs(j) → i ≤ i0 ⊦ j = 0

User applied rule cut formula

And obtained the following new goals

Proof step 4:
j < 0, j0 < j2, 0 ≤ j0, i0 < i, abs(j) ≤ j2, j0 < abs(j), abs(j) * i ≤ abs(j) * i0 + j0, 0 < j2, ∀ j, i, i0, j0. abs(j) < j2 → abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 ∧ j0 < abs(j) → i ≤ i0 ⊦ j = 0
Proof step 21:
j0 < j2, 0 ≤ j0, i0 < i, abs(j) ≤ j2, j0 < abs(j), abs(j) * i ≤ abs(j) * i0 + j0, 0 < j2, ∀ j, i, i0, j0. abs(j) < j2 → abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 ∧ j0 < abs(j) → i ≤ i0 ⊦ j < 0, j = 0

Rule argument

fma: j < 0

Additional information

Used formulas: j < 0