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Proof step 6 from proof noeth-modlep (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 7:
j0 < j2, 0 < j2, j < 0, i0 < i, j0 + j < 0, 0 ≤ j + j2, 0 ≤ j0, j * i0 ≤ j * i + j0, j0 < abs(j + 1) ∧ abs(j + 1) < j2 ∧ abs(j + 1) * i ≤ abs(j + 1) * i0 + j0 ∧ 0 ≤ j0 → i ≤ i0, ∀ j0, j, i, i0. j0 < abs(j) ∧ abs(j) < j2 ∧ abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 → i ≤ i0 ⊦ j = 0

Rule argument

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

Additional information

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