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Proof step 7 from proof ushort-band-01 (previous step)

s2i(sho) < 0, ~65536 ≤ s2i(sho) ⊦ (s2i(sho) + 1) % 256 + 255 = (s2i(sho) + 65536) % 256

User applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
s2i(sho) + 65536 = i * 256 + j ∧ 0 ≤ j ∧ j < 256 ∧ 0 ≤ i ∧ 0 < 256 ∧ 0 ≤ s2i(sho) + 65536, s2i(sho) < 0, ~65536 ≤ s2i(sho) ⊦ (s2i(sho) + 1) % 256 + 255 = j

Rule argument

seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0) subst: [i, j, i0, j0] → [s2i(sho) + 65536, 256, i, j] rotate: T spec: int-div inst: name: div-elim-pospos

Additional information

Used simplifier rules: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;%⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0); (elim) Used terms: s2i(sho) + 65536, 256, i, j