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Proof step 10 from proof square-ex (previous step)

(j + 1) * (j + 1) = i0 + 1, 0 < i0, 0 ≤ i0, j * j ≤ i0, 0 < j, (2 + j) * (2 + j) ≤ i0 + 1 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 12:
(j + 1) * (j + 1) = i0 + 1, 0 < i0, 0 ≤ i0, j * j ≤ i0, 0 < j, 2 * (2 + j) + j * (2 + j) ≤ i0 + 1 ⊦

Rule argument

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

Additional information

Used terms: 2 + j, j, 2