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Proof step 4 from proof estimate-01 (previous step)

i * i0 = i1 * j + j1 ∧ 0 ≤ j1 ∧ j1 < j ∧ 0 < i * i0, j < i, j0 < i0, i1 ≤ j0, 0 < i0, 0 < j, 0 < i, 1 < i, i1 < i0 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
i * i0 = i1 * j + j1, j1 < i, 0 ≤ j1, i1 < i0, j1 < j, 1 < i, 0 < i, 0 < j, 0 < i0, i1 ≤ j0, j0 < i0, j < i, j1 + 1 < i ⊦

Rule argument

Additional information

Used simplifier rules: succ-01: ⊦ i +1 = i + 1; from specification int-basic2%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%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