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Proof step 61 from proof two-even (previous step)

2 * i = 2 * j2 ^2 + (2 * i1)^2 + 4 * i1 + 1 + 2 * (2 * i1 + 1) * j2 ⊦ i = ((2 * i1 + 1) / 2)^2 + ((2 * j2 + 2 * i1 + 1) / 2)^2, (2 * i1 ^2 + 2 * i1) * 2 = (2 * i1)^2 + 4 * i1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 62:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 63:
2 * i = 2 * j2 ^2 + (2 * i1)^2 + 4 * i1 + 1 + 2 * (2 * i1 + 1) * j2 ⊦ i = ((2 * i1 + 1) / 2)^2 + ((2 * j2 + 2 * i1 + 1) / 2)^2, (2 * i1 ^2) * 2 + (2 * i1) * 2 = (2 * i1)^2 + 4 * i1

Rule argument

spec: int-mult inst: name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [2, 2 * i1, 2 * i1 ^2] flags: rewrite

Additional information

Used terms: 2, 2 * i1, 2 * i1 ^2