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Proof step 5 from proof noeth-modlep (previous step)

j0 + j < 0, 0 ≤ j + j2, j < 0, j * i0 ≤ j * i + j0, i0 < i, 0 ≤ j0, 0 < j2, j0 < 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 all left

And obtained the following new goals

Proof step 6:
j0 + j < 0, 0 ≤ j + j2, j < 0, j * i0 ≤ j * i + j0, i0 < i, 0 ≤ j0, 0 < j2, j0 < j2, abs(j + 1) < j2 → abs(j + 1) * i ≤ abs(j + 1) * i0 + j0 ∧ 0 ≤ j0 ∧ j0 < abs(j + 1) → i ≤ i0, ∀ j, i, i0, j0. abs(j) < j2 → abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 ∧ j0 < abs(j) → i ≤ i0 ⊦ j = 0

Rule argument

pos: left 9 terms: j + 1, i, i0, j0 abort: F discard: F computed: F

Additional information

Used terms: j + 1, i, i0, j0