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Proof step 34 from proof no-leading-zero (previous step)

int2bytes(bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) = i2b(0) ' + by ' + bytes1 + by0 ', bytes2int(i2b(0) ' + by ' + bytes1) ≤ 0, 0 ≤ band(b2i(by0), 255), 0 ≤ b2i(by), band(b2i(by0), 255) < 256, ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦ bytes2int(i2b(0) ' + by ' + bytes1) < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
bytes2int(i2b(0) ' + by ' + bytes1) = 0, int2bytes(band(b2i(by0), 255)) = i2b(0) ' + by ' + bytes1 + by0 ', band(b2i(by0), 255) < 256, 0 ≤ b2i(by), 0 ≤ band(b2i(by0), 255), i2b(0) ∈ int2bytes(band(b2i(by0), 255)), by0 ∈ int2bytes(band(b2i(by0), 255)), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + 0 = i;% ⊦ by ' + bytes = bytes0 → by ∈ bytes0; (forward)% ⊦ bytes + by ' = bytes0 → by ∈ bytes0; (forward)% ⊦ band(i, j) = band(j, i);% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ ¬ i < j ↔ j ≤ i;