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Proof step 10 from proof getInt-theorem (previous step)

⊦ bor(b2i(by3) i<< 24, bor(band(b2i(by2), 255) i<< 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) i<< 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 11:
⊦ 0 ≤ j ∧ j < 32 → i i<< j = i * 2 ^ j
Proof step 12:
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

Rule argument

seq: ⊦ 0 ≤ j ∧ j < 32 → i i<< j = i * 2 ^ j subst: [j, i] → [16, band(b2i(by2), 255)] rotate: F spec: intops inst: name: intshiftleft-is-mult

Additional information

Used terms: 16, band(b2i(by2), 255)