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Proof step 16 from proof exin2pot (previous step)

j = i0 * 2 + j1 ∧ 0 ≤ j1 ∧ j1 < 2 ∧ 0 < 2 ∧ 0 ≤ j, 0 ≤ i, 2 ^ i ≤ i0, i0 < 2 ^ (i + 1), 0 < j, 2 ^ i < 2 ^ (i + 1), ∀ j0. i→n(j0) < i→n(j) → 0 < j0 → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ j0 ∧ j0 < 2 ^ (i + 1)) ⊦ j = 1, j = 0, 0 ≤ i + 1 ∧ 2 ^ (i + 1) ≤ j ∧ j < 2 ^ (2 + i)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
0 ≤ i, 2 ^ i ≤ i0, i0 < 2 ^ (i + 1), 0 < i0 * 2 + j1, 2 ^ i < 2 ^ (i + 1), 0 ≤ j1, j1 < 2, 0 ≤ i0, 0 < 2 ^ (i + 1), ∀ j0. i→n(j0) < i→n(i0 * 2 + j1) → 0 < j0 → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ j0 ∧ j0 < 2 ^ (i + 1)) ⊦ i0 * 2 + j1 = 1, i0 * 2 + j1 = 0, 0 ≤ i + 1 ∧ 2 ^ (i + 1) ≤ i0 * 2 + j1 ∧ i0 * 2 + j1 < 2 ^ (2 + i)

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-ge-add: ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0); from specification int-mult