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Proof step 8 from proof mod-by6 (previous step)

(i0 * (i0 + 1) * (2 * i0 + 1)) % 6 = 0, 0 ≤ i0 ⊦ (6 * (i0 + 1) * (i0 + 1) + i0 * (i0 + 1) * (2 * i0 + 1)) % 6 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i % j = 0 ∧ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → (i + i0) % j = i0 % j
Proof step 10:
¬((6 * (i0 + 1) * (i0 + 1)) % 6 = 0 ∧ 0 ≤ 6 * (i0 + 1) * (i0 + 1) ∧ 0 ≤ i0 * (i0 + 1) * (2 * i0 + 1) ∧ 0 < 6), (i0 * (i0 + 1) * (2 * i0 + 1)) % 6 = 0, 0 ≤ i0 ⊦ (6 * (i0 + 1) * (i0 + 1) + i0 * (i0 + 1) * (2 * i0 + 1)) % 6 = 0

Rule argument

spec: inst: name: mod-add1-pospos seq: ⊦ i % j = 0 ∧ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → (i + i0) % j = i0 % j subst: [j, i0, i] → [6, i0 * (i0 + 1) * (2 * i0 + 1), 6 * (i0 + 1) * (i0 + 1)] flags: rewrite, current

Additional information

Used simplifier rules: associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 6, i0 * (i0 + 1) * (2 * i0 + 1), 6 * (i0 + 1) * (i0 + 1)