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Proof step 4 from proof auxexdivmod (previous step)

0 < j, i < (i0 + i2 +1) * j, 0 ≤ i2 +1, 0 ≤ i, 0 ≤ i0, i0 * j ≤ i, 0 < j ∧ i < (i0 + i2) * j ∧ 0 ≤ i2 ∧ 0 ≤ i ∧ 0 ≤ i0 ∧ i0 * j ≤ i → (∃ i0. i0 * j ≤ i ∧ i < (i0 + 1) * j ∧ 0 ≤ i0), ∀ j, i, i0. 0 < j ∧ i < (i0 + i2) * j ∧ 0 ≤ i2 ∧ 0 ≤ i ∧ 0 ≤ i0 ∧ i0 * j ≤ i → (∃ i0. i0 * j ≤ i ∧ i < (i0 + 1) * j ∧ 0 ≤ i0) ⊦ ∃ 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 7

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