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Proof step 19 from proof bytes2bytes-other (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ byte2bits(by) = fillsgn(8, int2bits(b2i(by)))
Proof step 21:
∀ bytes1. # bytes1 < #([] + by ') → bytes2bits(bytes1) ≠ [] → bytes1 = [] ∨ b2i(bytes1.first) = 0 ∨ b2i(bytes1.first) = ~1 ∨ bits2bytes(sgn(bytes2bits(bytes1))) = bytes1 ⊦ bits2bytes(sgn(fillsgn(8, int2bits(b2i(by))))) = by ', b2i(by) = ~1, b2i(by) = 0

Rule argument

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

Additional information

Used terms: by