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Proof step 14 from proof mod-neq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
i * j = i * j0 + j1, abs(j1) < i, j1 < i, 0 ≤ i ⊦ j1 = 0, 0 < j1 ∧ 0 < i

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i;% ⊦ ¬ i < i; (s)% ⊦ 0 ≤ i → abs(i) = i; (s)%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ 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)