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Proof step 5 from proof div-elim-negneg (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 6:
i1 * j + j1 = i0 * j + j0 ∧ j0 ≤ 0 ∧ j < j0 ∧ 0 ≤ i0, j < j1, j < 0, j1 ≤ 0, i1 * j + j1 < 0 ⊦ i0 = i1 ∧ j0 = j1

Rule argument

pos: right 1

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%modzero-04: ⊦ i < 0 ∧ j < j0 ∧ j < 0 → ¬ i * j + j0 < 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2