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Proof step 5 from proof band-mod256-neg (previous step)

i % 256 - 256 < 0 ∧ 0 ≤ 8 ⊦ 0 ≤ i ∧ 127 < i % 256 → ((i % 256 - 256) + 1) % 2 ^ 8 + 2 ^ 8 - 1 = i % 256

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
0 < i % 256, 127 < i % 256, 0 ≤ i ⊦ 255 + (~255 + i % 256) % 256 = i % 256

Rule argument

Additional information

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