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Proof step 4 from proof product-negative (previous step)

i * Π ints0 < 0, ∀ i0. i0 = i ∨ i0 ∈ ints0 → 0 ≤ i0 ⊦ Π ints0 < 0 ∧ (i0 ∈ ints0 → 0 ≤ i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 < i → (i * j < 0 ↔ j < 0)
Proof step 6:
¬ 0 < i, i * Π ints0 < 0, ∀ i0. i0 = i ∨ i0 ∈ ints0 → 0 ≤ i0 ⊦ Π ints0 < 0 ∧ (i0 ∈ ints0 → 0 ≤ i0)
Proof step 8:
0 < i, Π ints0 < 0, ∀ i0. i0 = i ∨ i0 ∈ ints0 → 0 ≤ i0 ⊦ Π ints0 < 0 ∧ (i0 ∈ ints0 → 0 ≤ i0)

Rule argument

spec: int-mult inst: name: zero-ls seq: ⊦ 0 < i → (i * j < 0 ↔ j < 0) subst: [j, i] → [Π ints0, i] flags: rewrite

Additional information

Used terms: Π ints0, i