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Proof step 26 from proof modby6-help (previous step)

⊦ i * (i * 7 + 6 + i * 2 * i) + 1 * (i * 7 + 6 + i * 2 * i) = 12 * i + 6 * i * i + 6 + i * (i + 1) * (2 * i + 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
⊦ ~4 * i * i + ~5 * i + i * (i * 7 + 6 + i * 2 * i) = i * (i + 1) * (2 * i + 1)

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%numadd: ⊦ i + (* j) = i0 + (* j0) ↔ i = i0 + (j0 - j); from specification int-abs%numeq: ⊦ (* i2) * i + j = (* i1) * i + j0 ↔ (i2 - i1) * i + j = j0; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult