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Proof step 8 from proof auxexdivmod (previous step)

0 < i2 * j + j, 0 < i0 * j + i2 * j + j, 0 < j, i < i0 * j + i2 * j + j, 0 ≤ i0, 0 ≤ i, i0 * j ≤ i, ~1 ≤ i2, ∀ 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) ⊦ i < i0 * j + i2 * j, ∃ i1. i1 * j ≤ i ∧ i < i1 * j + j ∧ 0 ≤ i1, i0 * j + i2 * j ≤ i ∧ 0 ≤ i0 + i2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
0 < i2 * j + j, 0 < i0 * j + i2 * j + j, i < i0 * j + i2 * j + j, 0 < j, i0 * j + i2 * j ≤ i, 0 ≤ i0, 0 ≤ i, i0 * j ≤ i, ~1 ≤ i2, ∀ 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) ⊦ 0 ≤ i0 + i2, ∃ i1. i1 * j ≤ i ∧ i < i1 * j + j ∧ 0 ≤ i1

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i < i + j ↔ 0 < j; (s)% ⊦ i + j < i + i0 ↔ j < i0; (s)%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs% ⊦ i < j ↔ ¬ j ≤ i; (ss)