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Proof step 32 from proof cast-mod-pos-high (previous step)

0 ≤ i - 1 ∧ 2 ^ (i - 1) ≤ j ∧ j < 2 ^ ((i - 1) + 1), i→n((i - 1) + 2) = i→n(i) + 1, 0 < i, 0 ≤ i, 2 ^ (i - 1) ≤ j % 2 ^ i, 0 ≤ j, 2 ^ (i - 1) ≤ j, 0 ≤ 2 ^ (i - 1) + j, j < 2 ^ i, 0 < j ⊦ j = j % 2 ^ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
0 ≤ i, 2 ^ (i - 1) ≤ j % 2 ^ i, 0 ≤ j, 2 ^ (i - 1) ≤ j, 0 ≤ 2 ^ (i - 1) + j, 0 < j, 0 < i, j < 2 ^ i ⊦ j = j % 2 ^ i

Rule argument

Additional information

Used simplifier rules: ⊦ i + (j - i) = j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ 0 < i → i→n(i + 1) = i→n(i) + 1;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ i + (j - i0) = i + j - i0;