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Proof step 29 from proof getInt-theorem (previous step)

0 ≤ band(b2i(by2), 255), 16777216 ≤ 65536 * band(b2i(by2), 255) + 256 * band(b2i(by1), 255), band(b2i(by1), 255) < 256, 0 < 65536 * band(b2i(by2), 255) + 256 * band(b2i(by1), 255), 0 ≤ 65536 * band(b2i(by2), 255) + 256 * band(b2i(by1), 255), 0 ≤ band(b2i(by1), 255) ⊦ 65536 * band(b2i(by2), 255) + 256 * band(b2i(by1), 255) < 65536 * band(b2i(by2), 255) + 256 * 256, bor(256 * band(b2i(by1), 255) + 65536 * band(b2i(by2), 255), 16777216 * b2i(by3)) = bytes2int(by3 ' + by2 ' + by1 ') * 256, bor(16777216 * b2i(by3), 65536 * band(b2i(by2), 255) + 256 * band(b2i(by1), 255)) = bytes2int(by3 ' + by2 ' + by1 ') * 256, bor(256 * band(b2i(by1), 255) + 65536 * band(b2i(by2), 255), bor(band(b2i(by0), 255), 16777216 * b2i(by3))) = bor(bytes2int(by3 ' + by2 ' + by1 ') * 256, band(b2i(by0), 255))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i + j < i + i0 ↔ j < i0 subst: [i0, j, i] → [256 * 256, 256 * band(b2i(by1), 255), 65536 * band(b2i(by2), 255)] rotate: F spec: int-basic2 inst: name: ls-01

Additional information

Used simplifier rules: ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 < (* j) ↔ i0 < (i + j - 1) / i);% ⊦ band(i, j) = band(j, i);%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: 256 * 256, 256 * band(b2i(by1), 255), 65536 * band(b2i(by2), 255)