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Proof step 3 from proof div-mult-02 (previous step)

i * i0 = i1 * j * i0 + j0 ∧ 0 ≤ j0 ∧ j0 < j * i0 ∧ 0 < j * i0 ∧ 0 ≤ i * i0, 0 < j, 0 < i0, 0 ≤ i ⊦ i1 = i / j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
i * i0 = i1 * j * i0 + j0, j0 < j * i0, 0 ≤ j0, 0 ≤ i, 0 < j, 0 < i0 ⊦ i1 = i / j

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%zero-ge: ⊦ 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%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult