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Proof step 15 from proof mod-neq (previous step)

i * j = i * j0 + j1, abs(j1) < i, j1 < i, 0 ≤ i ⊦ j1 = 0, 0 < j1 ∧ 0 < i

User applied rule apply lemma

And obtained the following new goals

Proof step 16:
i * j + j0 = i0 * j + j1, j0 ≤ 0, abs(j0) < j, j1 ≤ 0, abs(j1) < j ⊦ i = i0 ∧ j0 = j1
Proof step 17:
i * j = i * j0 + j1, j1 < i, abs(j1) < i, 0 ≤ i ⊦ j1 = 0, 0 < j1 ∧ 0 < i, j * i + 0 = j0 * i + j1 ∧ 0 ≤ 0 ∧ abs(0) < i ∧ j1 ≤ 0

Rule argument

spec: <toplevel> name: modeqp-01 seq: i * j + j0 = i0 * j + j1, j0 ≤ 0, abs(j0) < j, j1 ≤ 0, abs(j1) < j ⊦ i = i0 ∧ j0 = j1 subst: [i, j, j0, i0, j1] → [j, i, 0, j0, j1]

Additional information

Used terms: j, i, 0, j0, j1