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Proof step 40 from proof no-leading-zero (previous step)

byte2bits(i2b(0)) + byte2bits(by) + bytes2bits(bytes1) ≠ [], int2bytes(band(b2i(by0), 255)) = i2b(0) ' + by ' + bytes1 + by0 ', ¬ true ∈ byte2bits(i2b(0)) + byte2bits(by) + bytes2bits(bytes1), 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 41:
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 ⊦ byte2bits(i2b(0)) + byte2bits(by) + bytes2bits(bytes1) = [], true ∈ bytes2bits(bytes1), true ∈ byte2bits(by), true ∈ byte2bits(i2b(0))

Rule argument

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);