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Proof step 7 from proof auxexdivmod (previous step)

i < i0 * j + i2 * j + j, 0 < j, 0 < i0 * j + i2 * j + j, 0 < i2 * j + j, ~1 ≤ i2, i0 * j ≤ i, 0 ≤ i, 0 ≤ i0, ∀ j0, i1, i3. 0 < j0 ∧ i1 < i3 * j0 + i2 * j0 ∧ 0 ≤ i2 ∧ 0 ≤ i1 ∧ 0 ≤ i3 ∧ i3 * j0 ≤ i1 → (∃ i4. i4 * j0 ≤ i1 ∧ i1 < i4 * j0 + j0 ∧ 0 ≤ i4) ⊦ ∃ i1. i1 * j ≤ i ∧ i < i1 * j + j ∧ 0 ≤ i1, i < i0 * j + i2 * j ∧ 0 ≤ i2, i0 * j + i2 * j ≤ i ∧ 0 ≤ i0 + i2

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 2

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