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Proof step 123 from proof bytes2int-int2bytes-len-eq (previous step)

0 < 256 * (b2i(by0) + 1) + band(b2i(by), 255), b2i(by0) < 0, 256 * b2i(by0) + band(b2i(by), 255) < ~128, ~256 < 256 * b2i(by0) + band(b2i(by), 255), 256 * b2i(by0) + band(b2i(by), 255) < 0, ∀ bytes0. # bytes0 < #((by0 + []) + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ i2b(~1) = by0

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: ⊦ i < 0 ∧ j0 < j ∧ 0 < j → ¬ 0 ≤ i * j + j0 subst: [i, j0, j] → [b2i(by0) + 1, band(b2i(by), 255), 256] rotate: F spec: int-mult inst: name: modzero-03

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1);% ⊦ ¬ 256 ≤ band(i, 255);% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ b2i(by) = i → (i2b(i) ≠ by ↔ false); Used terms: b2i(by0) + 1, band(b2i(by), 255), 256