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Proof step 7 from proof div-rec (previous step)

j0 < j, 0 < j, 0 ≤ j0, 0 < j * (i1 + 1) + j0, 0 ≤ i1 ⊦ (j * (i1 + 1) + j0) / j = i1 + 1

User applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
⊦ 0 < j ∧ 0 < i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j)
Proof step 9:
j * (i1 + 1) + j0 = i0 * j + j1 ∧ 0 ≤ j1 ∧ j1 < j, j0 < j, 0 < j, 0 ≤ j0, 0 < j * (i1 + 1) + j0, 0 ≤ i1 ⊦ i0 = i1 + 1

Rule argument

spec: int-div inst: name: div-elim seq: ⊦ 0 < j ∧ 0 < i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j) subst: [i, j, i0, j0] → [j * (i1 + 1) + j0, j, i, j1] flags: current, []

Additional information

Used terms: j * (i1 + 1) + j0, j, i, j1