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Proof step 10 from proof fits-law-shr (previous step)

0 < band(i, 31), b2i(by) < 0 ⊦ b2i(by) i>> band(i, 31) = b2i(i2b(b2i(by) i>> band(i, 31)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ i < 0 ∧ 0 < j ∧ j < 32 → i i>> j = (i - (2 ^ j - 1)) / 2 ^ j
Proof step 12:
b2i(by) < 0 ∧ 0 < band(i, 31) ∧ band(i, 31) < 32, 0 < band(i, 31), b2i(by) < 0 ⊦ (b2i(by) - (2 ^ band(i, 31) - 1)) / 2 ^ band(i, 31) = b2i(i2b((b2i(by) - (2 ^ band(i, 31) - 1)) / 2 ^ band(i, 31)))

Rule argument

seq: ⊦ i < 0 ∧ 0 < j ∧ j < 32 → i i>> j = (i - (2 ^ j - 1)) / 2 ^ j subst: [j, i] → [band(i, 31), b2i(by)] rotate: F spec: intops inst: name: shiftrsign-2pot-neg-01

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ band(i, j) = band(j, i);% ⊦ 0 ≤ i ∧ i < i0 → ¬ i0 ≤ band(i, j);% ⊦ band(i, band(i0, j)) = band(band(i, i0), j); Used terms: band(i, 31), b2i(by)