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Proof step 2 from proof modeqp-neg (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
i * i0 + j0 = i1 * j + j1, i < 0, j0 < 0, j1 < 0, i1 < i, 0 < j + j0, 0 < j + j1, i0 ≤ j, 0 ≤ i0, 0 ≤ j ⊦

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-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ ~ i < j ↔ 0 < j + i; (s)% ⊦ i < 0 → abs(i) = ~ i; (s)