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Proof step 9 from proof div-add-succ (previous step)

i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0 ∧ 0 ≤ i, 0 < j, 1 < j, 0 < i, 0 ≤ j ⊦ j0 = 0, (i - 1) / j = i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
j0 < j, 0 < j, 0 ≤ j, 0 ≤ i0, 0 ≤ i0 * j + j0, 0 < i0 * j + j0, 0 < j0, 1 < j ⊦ j0 = 0, (i0 * j + j0 - 1) / j = i0

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs