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Proof step 11 from proof div-shift-two (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ i + j = j + i
Proof step 13:
j0 < j, 0 < j, 0 ≤ j0, 0 ≤ i0 ⊦ j = 0, i0 = (i0 * j + j0 < (1 + 2 * i0 / 2) * j ⊃ 0;1) + 2 * i0 / 2

Rule argument

spec: int-basic2 inst: name: add-c seq: ⊦ i + j = j + i subst: [j, i] → [(i0 * j + j0 < (1 + 2 * i0 / 2) * j ⊃ 0;1), 2 * i0 / 2] flags: rewrite

Additional information

Used terms: (i0 * j + j0 < (1 + 2 * i0 / 2) * j ⊃ 0;1), 2 * i0 / 2