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Proof step 10 from proof mod-pred-02 (previous step)

(i1 * j + j0) + 1 = i0 * j + j1, j0 < j, 0 ≤ j0, 0 ≤ i1, j1 < j, ~1 ≤ i1 * j + j0, 0 < j1, 1 < j, 0 < j ⊦ j1 = 0, j1 = j0 + 1

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 11:
i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1
Proof step 12:
(i1 * j + j0) + 1 = i0 * j + j1, j0 < j, 0 ≤ j0, 0 ≤ i1, j1 < j, ~1 ≤ i1 * j + j0, 0 < j1, 1 < j, 0 < j ⊦ i1 * j + j0 + 1 = i0 * j + j1 ∧ 0 ≤ j0 + 1 ∧ j0 + 1 < j ∧ 0 ≤ j1, j1 = 0, j1 = j0 + 1

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, j, j0 + 1, i0, j1] flags: []

Additional information

Used terms: i1, j, j0 + 1, i0, j1