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Proof step 16 from proof modeq-neg-02 (previous step)

j * (i1 + i0) + j1 = i2 * j + j0, 2 * j + j0 < j, j0 + j < j, abs(j0) < j, 1 < j, i2 * j + j0 < 0, i0 < 0, j1 < j, 0 < j1, 0 < j, j0 < j1, j0 < j, j0 + j < j1, 2 * j + j0 ≤ j1, j0 + j ≤ j1, j0 ≤ 0, 0 ≤ i1 * j + j1, j0 ≤ j1 ⊦ j0 = 0, j1 = j0 + j, j1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
j * (i1 + i0) + j1 = i2 * j + j0, 1 < j1, 0 < j + j0, 1 < j, i2 * j + j0 < 0, i0 < 0, j1 < j, 0 < j1, 0 < j, j0 < j1, j0 < j, j0 + j < j1, j0 < 0, 2 * j + j0 < j, j0 + j < j, 2 * j + j0 ≤ j1, 0 ≤ i1 * j + j1, j0 ≤ j1 ⊦ j0 = 0, j1 = j0 + j, j1 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%add-c: ⊦ i + j = j + i; from specification int-basic2%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)