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Proof step 48 from proof bytes2bytes-mone (previous step)

b2i(by0) = ~1, 0 ≤ b2i(by1), ∀ bytes1. # bytes1 < #((by0 + by1 + bytes0) + by ') → b2i(bytes1.first) = ~1 ∧ 0 ≤ b2i(bytes1.rest.first) → bits2bytes(sgn(bytes2bits(bytes1))) = bytes1 ∨ # bytes1 = 1 ∨ bytes1 = [] ⊦ bits2bytes(sgn(byte2bits(by0) + (byte2bits(by1) + bytes2bits(bytes0)) + byte2bits(by))) = by0 ' + (by1 ' + bytes0) + by ', (true ∈ byte2bits(by0) ∨ true ∈ byte2bits(by1) ∨ true ∈ bytes2bits(bytes0)) ∧ (false ∈ byte2bits(by0) ∨ false ∈ byte2bits(by1) ∨ false ∈ bytes2bits(bytes0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ byte2bits(by) = fillsgn(8, int2bits(b2i(by)))
Proof step 50:
b2i(by0) = ~1, 0 ≤ b2i(by1), ∀ bytes1. # bytes1 < #((by0 + by1 + bytes0) + by ') → b2i(bytes1.first) = ~1 ∧ 0 ≤ b2i(bytes1.rest.first) → bits2bytes(sgn(bytes2bits(bytes1))) = bytes1 ∨ # bytes1 = 1 ∨ bytes1 = [] ⊦ bits2bytes(sgn(fillsgn(8, int2bits(b2i(by0))) + (byte2bits(by1) + bytes2bits(bytes0)) + byte2bits(by))) = by0 ' + (by1 ' + bytes0) + by ', (true ∈ fillsgn(8, int2bits(b2i(by0))) ∨ true ∈ byte2bits(by1) ∨ true ∈ bytes2bits(bytes0)) ∧ (false ∈ fillsgn(8, int2bits(b2i(by0))) ∨ false ∈ byte2bits(by1) ∨ false ∈ bytes2bits(bytes0))

Rule argument

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

Additional information

Used terms: by0