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Proof step 24 from proof ushort-band-shift (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)
Proof step 26:
256 ≠ 0, ∃ j0. s2i(sho) = j0 * 256, s2i(sho) ≤ ~256, s2i(sho) < 0, ~65536 ≤ s2i(sho), 0 ≤ (65536 + s2i(sho)) / 256 ⊦ (s2i(sho) / 256 + 1) % 256 + 255 = ((65536 + s2i(sho)) / 256) % 256

Rule argument

seq: j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j) subst: [j, i] → [256, s2i(sho)] rotate: F spec: int-div inst: name: modex

Additional information

Used terms: 256, s2i(sho)