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Proof step 15 from proof getInt-theorem (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 0 ≤ j ∧ j < 32 → i i<< j = i * 2 ^ j

Rule argument

seq: ⊦ 0 ≤ j ∧ j < 32 → i i<< j = i * 2 ^ j subst: [j, i] → [8, band(b2i(by1), 255)] rotate: F spec: intops inst: name: intshiftleft-is-mult

Additional information

Used simplifier rules: ⊦ 0 < i ∧ 0 ≤ j → ((* j) ≤ (* i) * i0 ↔ (i + j - 1) / i ≤ i0);% ⊦ ¬ 256 ≤ band(i, 255);% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ 0 ≤ i → ¬ band(i, j) < 0; Used terms: 8, band(b2i(by1), 255)