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Proof step 20 from proof getInt-theorem (previous step)

band(b2i(by1), 255) i<< 8 < 65536, 0 ≤ band(b2i(by1), 255) i<< 8 ⊦ bor(b2i(by3) i<< 24, (band(b2i(by1), 255) i<< 8) + 65536 * band(b2i(by2), 255)) = bytes2int(by3 ' + by2 ' + by1 ') * 256, bor(65536 * band(b2i(by2), 255) + (band(b2i(by1), 255) i<< 8), bor(band(b2i(by0), 255), b2i(by3) i<< 24)) = bor(bytes2int(by3 ' + by2 ' + by1 ') * 256, band(b2i(by0), 255)), bor(b2i(by3) i<< 24, (band(b2i(by1), 255) i<< 8) + 65536 * band(b2i(by2), 255)) = bytes2int(by3 ' + by2 ' + by1 ') * 256

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ 0 ≤ j ∧ j < 32 → i i<< j = i * 2 ^ j
Proof step 22:
0 ≤ 24 ∧ 24 < 32, band(b2i(by1), 255) i<< 8 < 65536, 0 ≤ band(b2i(by1), 255) i<< 8 ⊦ bor(b2i(by3) * 2 ^ 24, (band(b2i(by1), 255) i<< 8) + 65536 * band(b2i(by2), 255)) = bytes2int(by3 ' + by2 ' + by1 ') * 256, bor(65536 * band(b2i(by2), 255) + (band(b2i(by1), 255) i<< 8), bor(band(b2i(by0), 255), b2i(by3) * 2 ^ 24)) = bor(bytes2int(by3 ' + by2 ' + by1 ') * 256, band(b2i(by0), 255)), bor(b2i(by3) * 2 ^ 24, (band(b2i(by1), 255) i<< 8) + 65536 * band(b2i(by2), 255)) = bytes2int(by3 ' + by2 ' + by1 ') * 256

Rule argument

seq: ⊦ 0 ≤ j ∧ j < 32 → i i<< j = i * 2 ^ j subst: [j, i] → [24, b2i(by3)] rotate: F spec: intops inst: name: intshiftleft-is-mult

Additional information

Used terms: 24, b2i(by3)