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Proof step 24 from proof cast-add-2pot-h (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
0 ≤ j + 2 ^ i, 2 ^ (i - 1) ≤ (j + 2 ^ i) % 2 ^ i, 0 < j + 2 ^ i, 0 < i, j < 0, 0 < 2 ^ i + j, 0 ≤ j + 2 ^ (i - 1) ⊦ (j + 2 ^ i) % 2 ^ i = j + 2 ^ i

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i - j = i0 ↔ i = i0 + j;