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Proof step 9 from proof noeth-zero-ls (previous step)

0 < i1, i * j < i, i * j < j, 0 < i, 0 < j, i * j < i1, i * j ≤ 0, i ≤ i1, ∀ j0, i0. 0 < j0 ∧ i0 ≠ 0 ∧ abs(i0) < i1 → 0 < abs(i0) * j0 ⊦

User applied rule all left

And obtained the following new goals

Proof step 10:
i * j < i1, 0 < j, 0 < i, i * j < j, i * j < i, 0 < i1, i ≤ i1, i * j ≤ 0, 0 < j ∧ i - 1 ≠ 0 ∧ abs(i - 1) < i1 → 0 < abs(i - 1) * j, ∀ j0, i0. 0 < j0 ∧ i0 ≠ 0 ∧ abs(i0) < i1 → 0 < abs(i0) * j0 ⊦

Rule argument

pos: left 9 terms: j, i - 1 abort: F discard: F computed: F

Additional information

Used terms: j, i - 1