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Proof step 84 from proof ushort-band-shift (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 85:
i = i0 * 256 + j0 ∧ j0 ≤ 0 ∧ abs(j0) < 256 ∧ i0 ≤ 0 ∧ 0 < 256 ∧ i < 0, i * 256 + j < 0, ~65536 ≤ i * 256 + j, ~256 < j, i ≤ 0, j < 0, ~256 ≤ j, ~255 ≤ i ⊦ j = 0, 255 + j0 = (i + 255) % 256

Rule argument

seq: ⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0) subst: [i, j, i0, j0] → [i, 256, i0, j0] rotate: T spec: int-div inst: name: div-elim-negpos

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);%⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0); (elim) Used terms: i, 256, i0, j0