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Proof step 60 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(false ' + byte2bits(by0) + bytes2bits(bytes0) + byte2bits(by1))) = by ' + by0 ' + bytes0 + by1 ', true ∈ byte2bits(by0), true ∈ bytes2bits(bytes0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 61:
⊦ byte2bits(by) = fillsgn(8, int2bits(b2i(by)))
Proof step 62:
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(false ' + fillsgn(8, int2bits(b2i(by0))) + bytes2bits(bytes0) + byte2bits(by1))) = by ' + by0 ' + bytes0 + by1 ', true ∈ fillsgn(8, int2bits(b2i(by0))), true ∈ bytes2bits(bytes0)

Rule argument

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

Additional information

Used terms: by0