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Proof step 30 from proof pot-square-est-02 (previous step)

(i1 + 1) * (i1 + 1) * 4 < 4 ^ i1 * 4, (i1 + 1) * (i1 + 1) < 4 ^ i1, 1 < i1, 0 < i1, (i1 + 1) * (i1 + 1) * 4 < 2 * (2 + i1) + i1 * (2 + i1), 4 ^ i1 * 4 ≤ 2 * (2 + i1) + i1 * (2 + i1), 0 ≤ i1, ∀ i0. i→n(i0) < i→n(i1 + 1) → 0 < i0 ∧ 1 < i0 ∧ 4 ^ i0 ≤ (i0 + 1) * (i0 + 1) → false ⊦ 2 * (2 + i1) + i1 * (2 + i1) = i1 * i1 + 4 * i1 + 4

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [i1, i1, 2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i * j + i * j0 = i * (j + j0); (s)% ⊦ i + i = 2 * i; (s)% ⊦ i * j + i = i * (j + 1); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i * (i0 + 1) + j = i + j0 ↔ i * i0 + j = j0; (s)% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); (s)%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i1, i1, 2