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Proof step 28 from proof band-011x-eq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
0 ≤ i0, j < 2 ^ i0, 0 ≤ j ⊦ 2 ^ i0 = (j % 2 ^ i0 + (2 ^ i0 - 1 + j) % 2 ^ i0) + 1

Rule argument

Additional information

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