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Proof step 16 from proof div-div-pred (previous step)

2 * (i1 * 2 + j1) + j0 = i0 * 4 + j2, abs(j2) < 4, abs(j1) < 2, j0 ≤ 0, abs(j0) < 2, i0 * 4 + j2 < ~3, j1 ≤ 0, i1 ≤ 0, i1 * 2 + j1 < 0, j2 ≤ 0, i0 ≤ 0, i0 * 4 + j2 < 0 ⊦ i1 = i0

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 17:
i * j + j0 = i0 * j + j1, j0 ≤ 0, abs(j0) < j, j1 ≤ 0, abs(j1) < j ⊦ i = i0 ∧ j0 = j1
Proof step 18:
2 * (i1 * 2 + j1) + j0 = i0 * 4 + j2, abs(j2) < 4, abs(j1) < 2, j0 ≤ 0, abs(j0) < 2, i0 * 4 + j2 < ~3, j1 ≤ 0, i1 ≤ 0, i1 * 2 + j1 < 0, j2 ≤ 0, i0 ≤ 0, i0 * 4 + j2 < 0 ⊦ i1 * 4 + 2 * j1 + j0 = i0 * 4 + j2 ∧ 2 * j1 + j0 ≤ 0 ∧ abs(2 * j1 + j0) < 4, i1 = i0

Rule argument

spec: int-mult inst: 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, 4, 2 * j1 + j0, i0, j2] flags: []

Additional information

Used terms: i1, 4, 2 * j1 + j0, i0, j2