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Proof step 3 from proof auxexdivmod (previous step)

i0 * j ≤ i ∧ i < (i0 + i2) * j ∧ 0 ≤ i0 ∧ 0 < j ∧ 0 ≤ i ∧ 0 ≤ i2 → (∃ i0. i0 * j ≤ i ∧ i < (i0 + 1) * j ∧ 0 ≤ i0), ∀ i0, j, i. i0 * j ≤ i ∧ i < (i0 + i2) * j ∧ 0 ≤ i0 ∧ 0 < j ∧ 0 ≤ i ∧ 0 ≤ i2 → (∃ i0. i0 * j ≤ i ∧ i < (i0 + 1) * j ∧ 0 ≤ i0), i0 * j ≤ i, i < (i0 + i2 +1) * j, 0 ≤ i0, 0 < j, 0 ≤ i, 0 ≤ i2 +1 ⊦ ∃ i0. i0 * j ≤ i ∧ i < (i0 + 1) * j ∧ 0 ≤ i0

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 1

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