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Proof step 6 from proof ushort-band (previous step)

¬ 0 ≤ i, 65536 ≤ band(i, 255), 0 < band(i, 255), 0 ≤ band(i, 255) ⊦ us2i(i2s(band(i, 255))) = band(i, 255)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
65281 ≤ (i + 1) % 256, i < 0, 0 < (i + 1) % 256, 0 ≤ (i + 1) % 256 ⊦ us2i(i2s((i + 1) % 256 + 255)) = (i + 1) % 256 + 255

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;%i0 ≠ 0, i0 < i ⊦ (* i) ≤ j → (* i0) < j;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ i < 0 → band(i, 255) = (i + 1) % 256 + 255;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ band(i, j) = band(j, i);