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Proof step 12 from proof getInt-theorem (previous step)

0 ≤ 16 ∧ 16 < 32 ⊦ bor(b2i(by3) i<< 24, bor(band(b2i(by2), 255) * 2 ^ 16, bor(band(b2i(by1), 255) i<< 8, band(b2i(by0), 255)))) = bor(bytes2int(by3 ' + by2 ' + by1 ') * 256, band(b2i(by0), 255)), bor(b2i(by3) i<< 24, bor(band(b2i(by2), 255) * 2 ^ 16, band(b2i(by1), 255) i<< 8)) = bytes2int(by3 ' + by2 ' + by1 ') * 256

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ j0 < 2 ^ i ∧ 0 ≤ i ∧ 0 ≤ j0 → bor(j * 2 ^ i, j0) = j * 2 ^ i + j0
Proof step 14:
¬(band(b2i(by1), 255) i<< 8 < 2 ^ 16 ∧ 0 ≤ 16 ∧ 0 ≤ band(b2i(by1), 255) i<< 8), 0 ≤ 16 ∧ 16 < 32 ⊦ bor(b2i(by3) i<< 24, bor(band(b2i(by2), 255) * 2 ^ 16, bor(band(b2i(by1), 255) i<< 8, band(b2i(by0), 255)))) = bor(bytes2int(by3 ' + by2 ' + by1 ') * 256, band(b2i(by0), 255)), bor(b2i(by3) i<< 24, bor(band(b2i(by2), 255) * 2 ^ 16, band(b2i(by1), 255) i<< 8)) = bytes2int(by3 ' + by2 ' + by1 ') * 256
Proof step 17:
band(b2i(by1), 255) i<< 8 < 2 ^ 16 ∧ 0 ≤ 16 ∧ 0 ≤ band(b2i(by1), 255) i<< 8, 0 ≤ 16 ∧ 16 < 32 ⊦ bor(b2i(by3) i<< 24, bor(band(b2i(by2), 255) * 2 ^ 16, bor(band(b2i(by1), 255) i<< 8, band(b2i(by0), 255)))) = bor(bytes2int(by3 ' + by2 ' + by1 ') * 256, band(b2i(by0), 255)), bor(b2i(by3) i<< 24, band(b2i(by2), 255) * 2 ^ 16 + (band(b2i(by1), 255) i<< 8)) = bytes2int(by3 ' + by2 ' + by1 ') * 256

Rule argument

seq: ⊦ j0 < 2 ^ i ∧ 0 ≤ i ∧ 0 ≤ j0 → bor(j * 2 ^ i, j0) = j * 2 ^ i + j0 subst: [j0, i, j] → [band(b2i(by1), 255) i<< 8, 16, band(b2i(by2), 255)] rotate: F spec: intops inst: name: bor-2pot-plus-02

Additional information

Used terms: band(b2i(by1), 255) i<< 8, 16, band(b2i(by2), 255)