[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 9 from proof ushort-band-shift (previous step)

0 ≤ (65536 + s2i(sho)) / 256, s2i(sho) < 0, ~65536 ≤ s2i(sho) ⊦ 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 10:
⊦ i < 0 ∧ i % 2 ^ j ≠ 0 ∧ 0 < j ∧ j < 32 → i i>> j = i / 2 ^ j - 1
Proof step 11:
¬(s2i(sho) < 0 ∧ s2i(sho) % 2 ^ 8 ≠ 0 ∧ 0 < 8 ∧ 8 < 32), 0 ≤ (65536 + s2i(sho)) / 256, s2i(sho) < 0, ~65536 ≤ s2i(sho) ⊦ band(s2i(sho) i>> 8, 255) = ((65536 + s2i(sho)) / 256) % 256
Proof step 67:
s2i(sho) < 0 ∧ s2i(sho) % 2 ^ 8 ≠ 0 ∧ 0 < 8 ∧ 8 < 32, 0 ≤ (65536 + s2i(sho)) / 256, s2i(sho) < 0, ~65536 ≤ s2i(sho) ⊦ band(s2i(sho) / 2 ^ 8 - 1, 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 - 1 subst: [j, i] → [8, s2i(sho)] rotate: F spec: intops inst: name: shiftrsign-2pot-neg-02

Additional information

Used terms: 8, s2i(sho)