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Proof step 8 from proof noeth-zero-ls (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 9:
0 < i, 0 < i1, i * j < i, i * j < j, i * j ≤ 0, 0 < j, i ≤ i1, i * j < i1, abs(i - 1) < i1 ∧ i - 1 ≠ 0 ∧ 0 < j → 0 < abs(i - 1) * j, ∀ i0, j0. abs(i0) < i1 ∧ i0 ≠ 0 ∧ 0 < j0 → 0 < abs(i0) * j0 ⊦

Rule argument

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

Additional information

Used terms: i - 1, j