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Proof step 4 from proof div-elim-negneg (previous step)

i = i1 * j + j1 ∧ j1 ≤ 0 ∧ j < j1, j < 0, i < 0 ⊦ i0 = i1 ∧ j0 = j1 ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ j < j0 ∧ 0 ≤ i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
j < j1, j < 0, j1 ≤ 0, i1 * j + j1 < 0 ⊦ i0 = i1 ∧ j0 = j1 ↔ i1 * j + j1 = i0 * j + j0 ∧ j0 ≤ 0 ∧ j < j0 ∧ 0 ≤ i0

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