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Proof step 3 from proof div2-nls-02 (previous step)

(i + j) / 2 < i, (i + j) / 2 < j, i ≤ j ⊦

User applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0)
Proof step 5:
(i + j) / 2 < j, (i + j) / 2 < i, i ≤ j ⊦ 0 < 2 ∧ 0 ≤ i + j
Proof step 16:
i + j = i0 * 2 + j0, i0 < j, i0 < i, j0 < 2, 0 < 2, i ≤ j, 0 ≤ j0, 0 ≤ i0, 0 ≤ i + j ⊦

Rule argument

spec: <toplevel> name: div-elim-pospos seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0) subst: [i, j, i0, j0] → [i + j, 2, i0, j0] flags: <rotated> <all paths>

Additional information

Used terms: i + j, 2, i0, j0