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Proof step 8 from proof mod-neq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
i * j = i * j0 + j1, i < 0, i < j1, 0 < j1, j1 + i < 0 ⊦ j1 = 0

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i;%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs% ⊦ 0 < j → abs(j) = j; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i ≤ j → (j < i ↔ false); (as)% ⊦ i - j < i0 ↔ i < j + i0; (s)% ⊦ i + ~ j = i - j; (s)% ⊦ i < 0 → abs(i) = ~ i; (s)%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs% ⊦ i < j ↔ ¬ j ≤ i; (ss)%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)