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Proof step 23 from proof fits-law-shr (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 24:
j ≠ 0 ⊦ ~ abs(i) ≤ i / j ∧ i / j ≤ abs(i)
Proof step 25:
~ abs(b2i(by) + 1) ≤ (b2i(by) + 1) / 2 ^ band(i, 31) ∧ (b2i(by) + 1) / 2 ^ band(i, 31) ≤ abs(b2i(by) + 1), (b2i(by) + 1) / 2 ^ band(i, 31) < ~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) < 0 ⊦ (b2i(by) + 1) / 2 ^ band(i, 31) = b2i(i2b((b2i(by) + 1) / 2 ^ band(i, 31) - 1)) + 1

Rule argument

seq: j ≠ 0 ⊦ ~ abs(i) ≤ i / j ∧ i / j ≤ abs(i) subst: [j, i] → [2 ^ band(i, 31), b2i(by) + 1] rotate: F spec: int-div inst: name: le-abs-numerator

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i);% ⊦ 0 ≤ j → 2 ^ j ≠ 0; Used terms: 2 ^ band(i, 31), b2i(by) + 1