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Proof step 47 from proof bytes2bytes-other (previous step)

8 = # byte2bits(by), ∀ bytes1. # bytes1 < #((by0 + bytes) + by ') → bytes2bits(bytes1) ≠ [] → bytes1 = [] ∨ b2i(bytes1.first) = 0 ∨ b2i(bytes1.first) = ~1 ∨ bits2bytes(sgn(bytes2bits(bytes1))) = bytes1 ⊦ b2i(by0) = ~1, b2i(by0) = 0, bits2bytes(sgn(byte2bits(by0) + bytes2bits(bytes))) + i2b(bits2int(byte2bits(by))) ' = (by0 ' + bytes) + by ', ¬ false ∈ byte2bits(by0) ∧ ¬ false ∈ bytes2bits(bytes), ¬ true ∈ byte2bits(by0) ∧ ¬ true ∈ bytes2bits(bytes)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
∀ bytes1. # bytes1 < #((by0 + bytes) + by ') → bytes2bits(bytes1) ≠ [] → bytes1 = [] ∨ b2i(bytes1.first) = 0 ∨ b2i(bytes1.first) = ~1 ∨ bits2bytes(sgn(bytes2bits(bytes1))) = bytes1 ⊦ b2i(by0) = ~1, b2i(by0) = 0, bits2bytes(sgn(byte2bits(by0) + bytes2bits(bytes))) = by0 ' + bytes, ¬ false ∈ byte2bits(by0) ∧ ¬ false ∈ bytes2bits(bytes), ¬ true ∈ byte2bits(by0) ∧ ¬ true ∈ bytes2bits(bytes)

Rule argument

Additional information

Used simplifier rules: byte2bits-length: ⊦ # byte2bits(by) = 8;%byte2bits-value: ⊦ bits2int(byte2bits(by)) = b2i(by);% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ bytes + bytes0 = bytes1 + bytes0 ↔ bytes = bytes1;% ⊦ i2b(b2i(by)) = by;