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Proof step 23 from proof pot-square-est-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ 1 * i = i
Proof step 25:
(i1 * 4 * i1 + 1 * 4 * i1) + (i1 + 1) * 4 < i1 * i1 + 4 * i1 + 4, (i1 * 4 * i1 + 1 * 4 * i1) + (i1 + 1) * 4 < 4 ^ i1 * 4, 4 ^ i1 * 4 ≤ i1 * i1 + 4 * i1 + 4, 0 ≤ i1, (i1 + 1) * (i1 + 1) < 4 ^ i1, 1 < i1, 0 < i1, ∀ i0. i→n(i0) < i→n(i1 + 1) → 4 ^ i0 ≤ (i0 + 1) * (i0 + 1) ∧ 0 < i0 ∧ 1 < i0 → false ⊦ (i1 * 4 * i1 + 1 * 4 * i1) + (i1 + 1) * 4 = 4 * i1 * i1 + 8 * i1 + 4

Rule argument

spec: int-mult inst: name: one seq: ⊦ 1 * i = i subst: [i] → [(i1 + 1) * 4] flags: rewrite

Additional information

Used terms: (i1 + 1) * 4