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Proof step 2 from proof zero-ls-03 (previous step)

i ≤ 0 ⊦ i * j < 0 ↔ 0 < j ∧ i ≠ 0

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ i < 0 → (i * j < i * j0 ↔ j0 < j)
Proof step 4:
i < 0 → (i * j < i * 0 ↔ 0 < j), i ≤ 0 ⊦ i * j < 0 ↔ 0 < j ∧ i ≠ 0

Rule argument

spec: int-mult inst: name: ls-neg seq: ⊦ i < 0 → (i * j < i * j0 ↔ j0 < j) subst: [i, j, j0] → [i, j, 0] flags: current, []

Additional information

Used terms: i, j, 0