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Proof step 8 from proof div-elim-negneg (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 9:
i * j + j0 = i0 * j + j1, j < 0, j0 ≤ 0, j < j0, j1 ≤ 0, j < j1 ⊦ i = i0 ∧ j0 = j1

Rule argument

spec: int-mult name: modeqp-03 seq: i * j + j0 = i0 * j + j1, j < 0, j0 ≤ 0, j < j0, j1 ≤ 0, j < j1 ⊦ i = i0 ∧ j0 = j1 subst: [i, j, j0, i0, j1] → [i1, j, j1, i0, j0]

Additional information

Used simplifier rules: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s) Used terms: i1, j, j1, i0, j0