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Proof step 33 from proof fits-law-shr (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 34:
⊦ i ≠ ~1 ∧ i ≠ 0 → b2i(by1) / i = b2i(i2b(b2i(by1) / i))
Proof step 35:
2 ^ band(i, 31) ≠ ~1 ∧ 2 ^ band(i, 31) ≠ 0 → b2i(by) / 2 ^ band(i, 31) = b2i(i2b(b2i(by) / 2 ^ band(i, 31))), band(i, 31) < 32, 0 ≤ b2i(by), 0 < band(i, 31) ⊦ b2i(by) / 2 ^ band(i, 31) = b2i(i2b(b2i(by) / 2 ^ band(i, 31)))

Rule argument

name: fits-law-div-stronger subst: [i, by1] → [2 ^ band(i, 31), by]

Additional information

Used terms: 2 ^ band(i, 31), by