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

s2i(sho) % 256 = 0, 0 ≤ (65536 + s2i(sho)) / 256, ~65536 ≤ s2i(sho), s2i(sho) < 0 ⊦ band(s2i(sho) i>> 8, 255) = ((65536 + s2i(sho)) / 256) % 256

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ i < 0 ∧ i % 2 ^ j = 0 ∧ 0 < j ∧ j < 32 → i i>> j = i / 2 ^ j
Proof step 14:
s2i(sho) < 0 ∧ s2i(sho) % 2 ^ 8 = 0 ∧ 0 < 8 ∧ 8 < 32, s2i(sho) % 256 = 0, 0 ≤ (65536 + s2i(sho)) / 256, ~65536 ≤ s2i(sho), s2i(sho) < 0 ⊦ band(s2i(sho) / 2 ^ 8, 255) = ((65536 + s2i(sho)) / 256) % 256

Rule argument

seq: ⊦ i < 0 ∧ i % 2 ^ j = 0 ∧ 0 < j ∧ j < 32 → i i>> j = i / 2 ^ j subst: [j, i] → [8, s2i(sho)] rotate: F spec: intops inst: name: shiftrsign-2pot-neg

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: 8, s2i(sho)