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Proof step 68 from proof ushort-band-shift (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 69:
⊦ i < 0 → band(i, 255) = (i + 1) % 256 + 255
Proof step 70:
s2i(sho) / 256 - 1 < 0, 0 ≤ (65536 + s2i(sho)) / 256, ~65536 ≤ s2i(sho), s2i(sho) < 0 ⊦ s2i(sho) % 256 = 0, ((s2i(sho) / 256 - 1) + 1) % 256 + 255 = ((65536 + s2i(sho)) / 256) % 256

Rule argument

seq: ⊦ i < 0 → band(i, 255) = (i + 1) % 256 + 255 subst: [i] → [s2i(sho) / 256 - 1] rotate: F spec: intops inst: name: band-255-neg

Additional information

Used simplifier rules: ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i < 1 ↔ i ≤ 0;% ⊦ 0 < j → (i / j ≤ 0 ↔ i < j);%j0 ≠ 0, j < j0 ⊦ i < (* j) → i < (* j0);% ⊦ band(i, j) = band(j, i); Used terms: s2i(sho) / 256 - 1