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Proof step 37 from proof no-leading-zero (previous step)

bits2int(bytes2bits(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 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
int2bytes(band(b2i(by0), 255)) = i2b(0) ' + by ' + bytes1 + by0 ', bits2int(byte2bits(i2b(0)) + byte2bits(by) + bytes2bits(bytes1)) = 0, 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: bytes2bits-rec: ⊦ bytes2bits(by ' + bytes) = byte2bits(by) + bytes2bits(bytes);% ⊦ band(i, j) = band(j, i);% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;