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Proof step 18 from proof pot-square-est-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-basic2 name: pls-01 seq: ¬ i < 0, ¬ j < 0 ⊦ ¬ i + j < 0 subst: [j, i] → [4 * i1, 3 * i1 * i1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 0 < i → (i * j < 0 ↔ j < 0); (s)% ⊦ i < j → ¬ j < i; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 4 * i1, 3 * i1 * i1