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Proof step 4 from proof noeth-modlep (previous step)

j0 < j2, i0 < i, j0 < abs(j), 0 < j2, abs(j) ≤ j2, 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 ⊦ j = 0

User applied rule cut formula

And obtained the following new goals

Proof step 5:
0 < j2, j0 < abs(j), i0 < i, j0 < j2, j < 0, abs(j) * i ≤ abs(j) * i0 + j0, 0 ≤ j0, abs(j) ≤ j2, ∀ j0, j, i, i0. j0 < abs(j) ∧ abs(j) < j2 ∧ abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 → i ≤ i0 ⊦ j = 0
Proof step 22:
0 < j2, j0 < abs(j), i0 < i, j0 < j2, abs(j) * i ≤ abs(j) * i0 + j0, 0 ≤ j0, abs(j) ≤ j2, ∀ j0, j, i, i0. j0 < abs(j) ∧ abs(j) < j2 ∧ abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 → i ≤ i0 ⊦ j = 0, j < 0

Rule argument

fma: j < 0

Additional information

Used formulas: j < 0