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Proof step 13 from proof ushort-band-01 (previous step)

j < 256, 0 ≤ i, 0 ≤ j, i * 256 + j < 65536 ⊦ 0 < 256 ∧ j + i * 256 - 65535 < 0, 255 + (j + i * 256 - 65535) % 256 = j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
0 < j + i * 256, 65535 ≤ j + i * 256, i * 256 + j < 65536, 0 ≤ j, 0 ≤ i, j < 256 ⊦ 255 + (j + i * 256 - 65535) % 256 = j

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0);% ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i - j < i0 ↔ i < j + i0;