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Proof step 18 from proof fits-law-shr (previous step)

0 ≤ band(i, 31), b2i(by) < ~1, b2i(by) < 0, 0 < band(i, 31), band(i, 31) < 32 ⊦ (b2i(by) + 1) / 2 ^ band(i, 31) = b2i(i2b((b2i(by) + 1) / 2 ^ band(i, 31) - 1)) + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ ~128 ≤ i ∧ i ≤ 127 → b2i(i2b(i)) = i
Proof step 20:
¬(~128 ≤ (b2i(by) + 1) / 2 ^ band(i, 31) - 1 ∧ (b2i(by) + 1) / 2 ^ band(i, 31) - 1 ≤ 127), 0 ≤ band(i, 31), b2i(by) < ~1, b2i(by) < 0, 0 < band(i, 31), band(i, 31) < 32 ⊦ (b2i(by) + 1) / 2 ^ band(i, 31) = b2i(i2b((b2i(by) + 1) / 2 ^ band(i, 31) - 1)) + 1

Rule argument

name: bib-in-01 rotate: F subst: [i] → [(b2i(by) + 1) / 2 ^ band(i, 31) - 1]

Additional information

Used simplifier rules: ⊦ i + (j - i) = j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: (b2i(by) + 1) / 2 ^ band(i, 31) - 1