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Proof step 44 from proof bytes2bytes-other (previous step)

bytes0 = by0 + bytes, false ∈ bytes2bits(bytes0), true ∈ bytes2bits(bytes0), ∀ bytes1. # bytes1 < #(bytes0 + by ') → bytes2bits(bytes1) ≠ [] → bytes1 = [] ∨ b2i(bytes1.first) = 0 ∨ b2i(bytes1.first) = ~1 ∨ bits2bytes(sgn(bytes2bits(bytes1))) = bytes1 ⊦ bits2bytes(sgn(bytes2bits(bytes0))) + i2b(bits2int(lastn(8, sgn(bytes2bits(bytes0)) + byte2bits(by)))) ' = bytes0 + by ', bytes0 = [], b2i(by0) = ~1, b2i(by0) = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
∀ 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(lastn(8, sgn(byte2bits(by0) + bytes2bits(bytes)) + byte2bits(by)))) ' = (by0 ' + bytes) + by ', ¬ false ∈ byte2bits(by0) ∧ ¬ false ∈ bytes2bits(bytes), ¬ true ∈ byte2bits(by0) ∧ ¬ true ∈ bytes2bits(bytes)

Rule argument

Additional information

Used simplifier rules: bytes2bits-append: ⊦ bytes2bits(bytes + bytes0) = bytes2bits(bytes) + bytes2bits(bytes0);%bytes2bits-one: ⊦ bytes2bits(by ') = byte2bits(by);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ by ' + bytes ≠ [];% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ by + bytes = by ' + bytes;