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Proof step 16 from proof bytes2bytes-zero (previous step)

b2i(by) = 0, b2i(by0) < 0, ∀ by0, by, bytes0. # bytes0 < # [] → b2i(by) = 0 ∧ b2i(by0) < 0 → bits2bytes(sgn(byte2bits(by) + byte2bits(by0) + bytes2bits(bytes0))) = by ' + by0 ' + bytes0 ⊦ bits2bytes(sgn(byte2bits(by) + byte2bits(by0))) = by ' + by0 '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ byte2bits(by) = fillsgn(8, int2bits(b2i(by)))
Proof step 18:
b2i(by) = 0, b2i(by0) < 0, ∀ by0, by, bytes0. # bytes0 < # [] → b2i(by) = 0 ∧ b2i(by0) < 0 → bits2bytes(sgn(byte2bits(by) + byte2bits(by0) + bytes2bits(bytes0))) = by ' + by0 ' + bytes0 ⊦ bits2bytes(sgn(fillsgn(8, int2bits(b2i(by))) + byte2bits(by0))) = by ' + by0 '

Rule argument

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

Additional information

Used terms: by