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Proof step 8 from proof mult-02 (previous step)

(i1 * j0 + j1) * j + i0 = i2 * j0 * j + j2, j2 < j0 * j, 0 ≤ j1, 0 ≤ i1, j1 < j0, 0 ≤ i0, i0 < j, 0 < j0, 0 ≤ j2, 0 < j ⊦ i2 = i1

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 9:
i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1
Proof step 10:
(i1 * j0 + j1) * j + i0 = i2 * j0 * j + j2, j2 < j0 * j, 0 ≤ j1, 0 ≤ i1, j1 < j0, 0 ≤ i0, i0 < j, 0 < j0, 0 ≤ j2, 0 < j ⊦ i1 * j0 * j + j1 * j + i0 = i2 * j0 * j + j2 ∧ 0 ≤ j1 * j + i0 ∧ j1 * j + i0 < j0 * j, i2 = i1

Rule argument

spec: int-mult inst: name: modeqp seq: i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1 subst: [i, j, j0, i0, j1] → [i1, j0 * j, j1 * j + i0, i2, j2] flags: []

Additional information

Used terms: i1, j0 * j, j1 * j + i0, i2, j2