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Proof step 68 from proof bytes2bytes-zero (previous step)

b2i(by) = 0, b2i(by0) < 0, ∀ by0, by, bytes1. # bytes1 < #(bytes0 + by1 ') → b2i(by) = 0 ∧ b2i(by0) < 0 → bits2bytes(sgn(byte2bits(by) + byte2bits(by0) + bytes2bits(bytes1))) = by ' + by0 ' + bytes1 ⊦ bits2bytes(sgn(byte2bits(by) + byte2bits(by0) + bytes2bits(bytes0))) + i2b(bits2int(lastn(8, sgn(byte2bits(by) + byte2bits(by0) + bytes2bits(bytes0)) + byte2bits(by1)))) ' = by ' + by0 ' + bytes0 + by1 ', byte2bits(by) + byte2bits(by0) + bytes2bits(bytes0) = [], ¬ true ∈ byte2bits(by) ∧ ¬ true ∈ byte2bits(by0) ∧ ¬ true ∈ bytes2bits(bytes0), ¬ false ∈ byte2bits(by) ∧ ¬ false ∈ byte2bits(by0) ∧ ¬ false ∈ bytes2bits(bytes0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ n = # bits → lastn(n, bits0 + bits) = bits subst: [bits, bits0, n] → [byte2bits(by1), sgn(byte2bits(by) + byte2bits(by0) + bytes2bits(bytes0)), 8] rotate: F spec: list-del inst: bitlista name: lastN-append

Additional information

Used simplifier rules: byte2bits-length: ⊦ # byte2bits(by) = 8; Used terms: byte2bits(by1), sgn(byte2bits(by) + byte2bits(by0) + bytes2bits(bytes0)), 8