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Proof step 11 from proof noeth-zero-ls (previous step)

∀ i, j. abs(i) < i1 ∧ 0 < abs(i) ∧ 0 < j → 0 < abs(i) * j, abs(i) < i1 -1, 0 < abs(i), 0 < j ⊦ 0 < abs(i) * j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
abs(i) + 1 < i1, 0 < j, abs(i) * j ≤ 0, abs(i) * j < j, ∀ i0, j0. abs(i0) < i1 ∧ i0 ≠ 0 ∧ 0 < j0 → 0 < abs(i0) * j0 ⊦ i = 0

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%abs-06: ⊦ 0 < abs(i) ↔ i ≠ 0; from specification int-abs%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%sub-pred: ⊦ i -1 = i - 1; from specification int-abs