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Proof step 22 from proof band-011x-eq (previous step)

0 ≤ i, 0 ≤ j, 0 < j, i < j ⊦ j % (i + 1) + (1 + i - j) % (i + 1) = 0, ∀ i0. i ≠ 2 ^ i0 - 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
0 ≤ j, 0 < j, 2 ^ i0 ≤ j, 0 ≤ i0 ⊦ (2 ^ i0 - j) % 2 ^ i0 + j % 2 ^ i0 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + (j - i) = j;