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Proof step 2 from proof mod-by6 (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 3:
0 ≤ i0 → (i0 * (i0 + 1) * (2 * i0 + 1)) % 6 = 0, 0 ≤ i0 +1 ⊦ (i0 +1 * (i0 +1 + 1) * (2 * i0 +1 + 1)) % 6 = 0
Proof step 13:
0 ≤ i0 → (i0 * (i0 + 1) * (2 * i0 + 1)) % 6 = 0, 0 ≤ i0 -1 ⊦ (i0 -1 * (i0 -1 + 1) * (2 * i0 -1 + 1)) % 6 = 0

Rule argument

indvar: i

Additional information

Used simplifier rules: int generated by 0, +1, -1;;%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult