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Proof step 9 from proof div-shift-two (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

spec: int-mult inst: name: commutativity seq: ⊦ i * j = j * i subst: [j, i] → [1 + 2 * i0 / 2, j] flags: rewrite

Additional information

Used terms: 1 + 2 * i0 / 2, j