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Proof step 98 from proof ushort-band-shift (previous step)

i * 256 - 255 = (i - 1) * 256 + 1, j0 = (i * 256 - 255) + j1, 255 + j0 = i * 256 + j1, 0 ≤ i, 0 ≤ j1, 256 * j0 + j < 0, j0 < 0, ~255 ≤ j0, ~256 ≤ j, j < 0, ~256 < j, ~65536 ≤ 256 * j0 + j, j1 < 256 ⊦ i = 0, 255 + j0 = j1, j = 0

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: discard

Additional information

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