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Proof step 23 from proof div-eq-zero-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
j0 < i0, 0 < i0, j < i0 * j + j0, j < 0, j < j0, j ≤ i0 * j + j0, j0 ≤ 0 ⊦ i0 = 0

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%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ i < 0 ∧ j0 < j ∧ 0 < j → i * j + j0 < 0; (s)%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)