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Proof step 5 from proof le-2pot (previous step)

2 ^ i ≤ j / 2, 0 ≤ j, 0 ≤ i ⊦ 2 ^ (i + 1) ≤ j

User applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
j = i0 * 2 + j0, j0 < 2, 0 < 2, 0 ≤ i, 0 ≤ j, 2 ^ i ≤ i0, 0 ≤ j0 ⊦ 2 ^ (i + 1) ≤ j

Rule argument

spec: int-div name: div-elim-pos 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, 2, i0, j0]

Additional information

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