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Proof step 27 from proof exin2pot (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
j1 < 2, i0 < 2 ^ i * 2, 0 < i0 * 2 + j1, 0 < i0, 2 ^ (2 + i) ≤ i0 * 2 + j1, 0 ≤ j1, 0 ≤ i, 2 ^ i ≤ i0, 0 ≤ i0, ∀ j0. i→n(j0) < i→n(i0 * 2 + j1) → 0 < j0 → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ j0 ∧ j0 < 2 ^ (i + 1)) ⊦ i0 * 2 + j1 = 0, i0 * 2 + j1 = 1

Rule argument

Additional information

Used simplifier rules: pot2-pos: ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ 0 < i → (0 < i * j ↔ 0 < j); (s)%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1% ⊦ i < j ↔ ¬ j ≤ i; (ss)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ 0 < i ∧ 0 ≤ j → ((* j) < (* i) * i0 ↔ j / i < i0); (s)% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)