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Proof step 12 from proof ushort-band-01 (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
j < 256, 0 ≤ i, 0 ≤ j, i * 256 + j < 65536 ⊦ 0 < 256 ∧ j + i * 256 - 65535 < 0, 255 + (j + i * 256 - 65535) % 256 = j
Proof step 20:
j + i * 256 - 65535 = i0 * 256 + j0 ∧ j0 ≤ 0 ∧ abs(j0) < 256 ∧ i0 ≤ 0 ∧ 0 < 256 ∧ j + i * 256 - 65535 < 0, j < 256, 0 ≤ i, 0 ≤ j, i * 256 + j < 65536 ⊦ 255 + j0 = j

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] → [j + i * 256 - 65535, 256, i0, j0] rotate: T spec: int-div inst: name: div-elim-negpos

Additional information

Used simplifier rules: ⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0); (elim) Used terms: j + i * 256 - 65535, 256, i0, j0