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Proof step 17 from proof pot-square-est-02 (previous step)

3 * i1 * i1 + 4 * i1 < 0, 0 < i1, 1 < i1, (i1 + 1) * (i1 + 1) < 4 ^ i1, 0 ≤ i1, 4 ^ i1 * 4 ≤ i1 * i1 + 4 * i1 + 4, 4 * i1 * i1 + 8 * i1 + 4 < 4 ^ i1 * 4, (3 * i1 * i1 + 4 * i1) + 1 < i1, ∀ i0. i→n(i0) < i→n(i1 + 1) → 4 ^ i0 ≤ (i0 + 1) * (i0 + 1) ∧ 0 < i0 ∧ 1 < i0 → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: zero-gs seq: ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i + j < 0 subst: [j, i] → [4 * i1, 3 * i1 * i1] flags: rewrite

Additional information

Used simplifier rules: zero-ge-02: ⊦ 0 ≤ i → (0 ≤ i * j ↔ ¬ ¬(i = 0 ∨ 0 ≤ j)); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: 4 * i1, 3 * i1 * i1