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Proof step 17 from proof mod-neq (previous step)

i * j = i * j0 + j1, j1 < i, abs(j1) < i, 0 ≤ i ⊦ j1 = 0, 0 < j1 ∧ 0 < i, j * i + 0 = j0 * i + j1 ∧ 0 ≤ 0 ∧ abs(0) < i ∧ j1 ≤ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
i * j = i * j0 + j1, abs(j1) < i, j1 < i, 0 ≤ i ⊦ j1 = 0, 0 < j1 ∧ 0 < i, 0 < i ∧ j1 < 0

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i;% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i + 0 = i; (s)