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Proof step 6 from proof diveq-neg (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 7:
i * j + j0 = i0 * j + j1, j0 ≤ 0, abs(j0) < j, j1 ≤ 0, abs(j1) < j ⊦ i = i0 ∧ j0 = j1

Rule argument

spec: int-mult name: modeqp-01 seq: i * j + j0 = i0 * j + j1, j0 ≤ 0, abs(j0) < j, j1 ≤ 0, abs(j1) < j ⊦ i = i0 ∧ j0 = j1 subst: [i, j, j0, i0, j1] → [i1, j, j1, i0, j0]

Additional information

Used terms: i1, j, j1, i0, j0