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Proof step 11 from proof mod-neq (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 12:
i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1
Proof step 13:
i * j = i * j0 + j1, abs(j1) < i, 0 ≤ i ⊦ j * i + 0 = j0 * i + j1 ∧ 0 ≤ 0 ∧ 0 < i ∧ 0 ≤ j1 ∧ j1 < i, j1 = 0

Rule argument

spec: int-mult inst: name: modeqp seq: i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1 subst: [i, j, j0, i0, j1] → [j, i, 0, j0, j1] flags: current, []

Additional information

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