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Proof step 10 from proof mod-pred-neg-01 (previous step)

i0 * j + j0 = i1 + 1, i1 = i2 * j + j1, i1 < 0, i1 < ~1, abs(j0) < j, 0 < j, i0 < j, j0 < j, abs(j1) < j, i0 ≤ 0, j0 ≤ 0, j1 ≤ 0, i2 ≤ 0 ⊦ j0 = j1 + 1, j1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
i0 * j + j0 = (i2 * j + j1) + 1, j0 < j, i0 < j, 0 < j, abs(j0) < j, i2 * j + j1 < ~1, i2 * j + j1 < 0, i2 < j, i2 < j + j1, j1 < 0, j0 < j + j1, i0 < j + j1, 0 < j + j1, j0 ≤ 0, i0 ≤ 0, i2 ≤ 0 ⊦ j0 = j1 + 1, j1 = 0

Rule argument

Additional information

Used simplifier rules: forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-le-02: ⊦ 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-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs% ⊦ ~ i < j ↔ 0 < j + i; (s)% ⊦ i < 0 → abs(i) = ~ i; (s)% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)