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Proof step 1 from proof square-zero-02 (conclusion)

⊦ 0 ≤ j ∧ 0 ≤ i → ¬ (i + j) * (i + j + 1) < 0

User applied rule insert lemma

And obtained the following new goals

Proof step 2:
⊦ 0 ≤ i → ¬ (i + 1) * (i + 2) ≤ 0
Proof step 3:
0 ≤ i + j - 1 → ¬ ((i + j - 1) + 1) * ((i + j - 1) + 2) ≤ 0 ⊦ 0 ≤ j ∧ 0 ≤ i → ¬ (i + j) * (i + j + 1) < 0

Rule argument

spec: inst: name: square-zero-01 seq: ⊦ 0 ≤ i → ¬ (i + 1) * (i + 2) ≤ 0 subst: [i] → [i + j - 1] flags: current, []

Additional information

Used terms: i + j - 1