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Proof step 9 from proof square-nls (previous step)

j * (j + 1) = i0 * 2 + j0, 0 < j, i0 < j, j0 < 2, j * (j + 1) < (i0 + 1) * 2, 0 ≤ j0, 0 ≤ i0, 0 ≤ j ⊦ j = 0, j * (j + 1) < j * (i0 + 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ i * j = j * i
Proof step 11:
j * (j + 1) = i0 * 2 + j0, j * (j + 1) < (i0 + 1) * 2, j0 < 2, i0 < j, 0 < j, 0 ≤ j, 0 ≤ i0, 0 ≤ j0 ⊦ j = 0, j * (j + 1) < (i0 + 1) * j

Rule argument

spec: int-mult name: commutativity seq: ⊦ i * j = j * i subst: [j, i] → [i0 + 1, j] flags: <all paths>

Additional information

Used terms: i0 + 1, j