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Proof step 14 from proof div2-nls-02 (previous step)

i + j = i0 * 2 + j0, abs(j0) < 2, i0 < i, i + j < 0, i0 < j, i ≤ j, i0 ≤ 0, j0 ≤ 0 ⊦ j0 = ~1, j0 < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
i + j = i0 * 2, i0 < j, i0 < i, i0 < 0, i ≤ j ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; (s)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ 0 < i → (i * j < 0 ↔ j < 0); (s)%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%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)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)%j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0); (s)% ⊦ ¬ j < 0 → abs(j) = j; (s)