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

0 < j, i < (i + j) / 2, i < j, 0 < (i + j) / 2, j ≤ (i + j) / 2, 0 ≤ i ⊦

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 = i0 * 2 + j0, 0 < i0, i < j, i < i0, 0 < j, j0 < 2, 0 < 2, 0 ≤ i, j ≤ i0, 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 simplifier rules: lstwozero: ⊦ i < 0 → ¬ 0 < i / 2;% ⊦ i ≤ j ↔ ¬ j < i; (ss) Used terms: i + j, 2, i0, j0