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Proof step 9 from proof modeqp (previous step)

i1 -1 * j + j0 = i0 * j + j1, j0 < j, j1 < j, 0 < j, 0 ≤ j0, 0 ≤ j1, ∀ j, j0, i0, j1. i1 * j + j0 = i0 * j + j1 ∧ j0 < j ∧ j1 < j ∧ 0 < j ∧ 0 ≤ j0 ∧ 0 ≤ j1 → i1 = i0 ∧ j0 = j1 ⊦ i0 + 1 = i1 ∧ j0 = j1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
i * j + j0 = i0 * j + j1, i1 = i +1, 0 < j, j1 < j, j0 < j, 0 ≤ j1, 0 ≤ j0, ∀ j, j0, i0, j1. i1 * j + j0 = i0 * j + j1 ∧ j0 < j ∧ j1 < j ∧ 0 < j ∧ 0 ≤ j0 ∧ 0 ≤ j1 → i1 = i0 ∧ j0 = j1 ⊦ i0 + 1 = i1 ∧ j0 = j1

Rule argument

spec: int-basic1 name: elim-pred seq: ⊦ i = j -1 ↔ j = i +1 subst: [j, i] → [i1, i]

Additional information

Used simplifier rules: ⊦ i = j -1 ↔ j = i +1; (elim) Used terms: i1, i