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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ i * j = j * i
Proof step 12:
j * (j + 1) < (i0 + 1) * 2, j * (j + 1) = i0 * 2 + j0, j0 < 2, i0 ≤ j, 0 ≤ j, 2 ≤ j, 0 < j, 0 ≤ j0, j0 < j, 0 ≤ i0 ⊦ j * (j + 1) < (i0 + 1) * j, j = 0

Rule argument

spec: int-mult inst: name: commutativity seq: ⊦ i * j = j * i subst: [j, i] → [i0 + 1, j] flags: rewrite

Additional information

Used terms: i0 + 1, j