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Proof step 4 from proof ushort-band-shift (previous step)

s2i(sho) < 0 ⊦ band(s2i(sho) i>> 8, 255) = band(255, (65536 + s2i(sho)) i>> 8)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 ≤ i ∧ 0 < j ∧ j < 32 → i i>> j = i / 2 ^ j
Proof step 6:
0 ≤ 65536 + s2i(sho) ∧ 0 < 8 ∧ 8 < 32, s2i(sho) < 0 ⊦ band(s2i(sho) i>> 8, 255) = band(255, (65536 + s2i(sho)) / 2 ^ 8)

Rule argument

seq: ⊦ 0 ≤ i ∧ 0 < j ∧ j < 32 → i i>> j = i / 2 ^ j subst: [j, i] → [8, 65536 + s2i(sho)] rotate: F spec: intops inst: name: shiftrsign-2pot-pos

Additional information

Used simplifier rules: short-min-02: ⊦ i ≤ ~32768 → ¬ s2i(sho) < i;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: 8, 65536 + s2i(sho)