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Proof step 4 from proof noeth-zero-ls (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ¬ j < 0 → abs(j) = j
Proof step 6:
i < 0, abs(i) * j < j, 0 < j, abs(i) * j ≤ 0, abs(i) ≤ i1, ∀ j0, i0. 0 < j0 ∧ i0 ≠ 0 ∧ abs(i0) < i1 → 0 < abs(i0) * j0 ⊦ i = 0
Proof step 8:
i * j < j, 0 < j, i * j ≤ 0, i ≤ i1, ∀ j0, i0. 0 < j0 ∧ i0 ≠ 0 ∧ abs(i0) < i1 → 0 < abs(i0) * j0 ⊦ i = 0, i < 0

Rule argument

spec: int-abs name: Abs-pos seq: ⊦ ¬ j < 0 → abs(j) = j subst: [j] → [i] flags: <all paths>

Additional information

Used terms: i