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Proof step 29 from proof bytes2bytes-other (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ byte2bits(by) = fillsgn(8, int2bits(b2i(by)))
Proof step 31:
∀ bytes1. # bytes1 < #((by0 + bytes) + by ') → bytes2bits(bytes1) ≠ [] → bytes1 = [] ∨ b2i(bytes1.first) = 0 ∨ b2i(bytes1.first) = ~1 ∨ bits2bytes(sgn(bytes2bits(bytes1))) = bytes1 ⊦ b2i(by0) = 0, b2i(by0) = ~1, bits2bytes(sgn((fillsgn(8, int2bits(b2i(by0))) + bytes2bits(bytes)) + byte2bits(by))) = (by0 ' + bytes) + by ', (true ∈ fillsgn(8, int2bits(b2i(by0))) ∨ true ∈ bytes2bits(bytes)) ∧ (false ∈ fillsgn(8, int2bits(b2i(by0))) ∨ false ∈ bytes2bits(bytes))

Rule argument

name: byte2bits rotate: F subst: [by] → [by0]

Additional information

Used terms: by0