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Proof step 4 from proof div-ls (previous step)

j ≠ 0, ∃ j0. i0 = j0 * j, j0 ≤ i / j, i < i0, i0 / j ≤ j0, 0 < j, 0 ≤ i, 0 < i0, i0 / j ≤ i / j ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
j1 ≤ i / j, 0 ≤ i, j1 ≤ j0, i < j1 * j, j0 ≤ i / j, 0 < i / j, 0 < j1, 0 < j0, 0 < j ⊦ j = 0

Rule argument

Additional information

Used simplifier rules: div-mult-03: j ≠ 0 ⊦ (i * j) / j = i;%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult