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Proof step 13 from proof fits-law-shr-01 (previous step)

0 ≤ (s2i(sho) i>> band(i, 31)) + s2i(sho), s2i(sho) i>> band(i, 31) < 0, 0 < s2i(sho) ⊦ s2i(sho) i>> band(i, 31) = s2i(i2s(s2i(sho) i>> band(i, 31)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ 0 ≤ j ∧ j < 32 → (i i>> j < 0 ↔ i < 0)

Rule argument

seq: ⊦ 0 ≤ j ∧ j < 32 → (i i>> j < 0 ↔ i < 0) subst: [j, i] → [band(i, 31), s2i(sho)] rotate: F spec: intops inst: name: right-ls-01

Additional information

Used simplifier rules: ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 ≤ i ∧ i < i0 → ¬ i0 ≤ band(i, j); Used terms: band(i, 31), s2i(sho)