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Proof step 14 from proof bytes2bytes-mone (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ bytes ≠ [] → (bytes + bytes0).first = bytes.first
Proof step 16:
¬ bytes0.rest ≠ [], b2i(bytes0.first) = ~1, 0 ≤ b2i((bytes0.rest + by ').first), ∀ bytes1. # bytes1 < #(bytes0 + by ') → b2i(bytes1.first) = ~1 ∧ 0 ≤ b2i(bytes1.rest.first) → bits2bytes(sgn(bytes2bits(bytes1))) = bytes1 ∨ # bytes1 = 1 ∨ bytes1 = [] ⊦ bits2bytes(sgn(bytes2bits(bytes0) + byte2bits(by))) = bytes0 + by ', bytes0 = [], true ∈ bytes2bits(bytes0) ∧ false ∈ bytes2bits(bytes0)
Proof step 43:
bytes0.rest ≠ [], b2i(bytes0.first) = ~1, 0 ≤ b2i(bytes0.rest.first), ∀ bytes1. # bytes1 < #(bytes0 + by ') → b2i(bytes1.first) = ~1 ∧ 0 ≤ b2i(bytes1.rest.first) → bits2bytes(sgn(bytes2bits(bytes1))) = bytes1 ∨ # bytes1 = 1 ∨ bytes1 = [] ⊦ bits2bytes(sgn(bytes2bits(bytes0) + byte2bits(by))) = bytes0 + by ', bytes0 = [], true ∈ bytes2bits(bytes0) ∧ false ∈ bytes2bits(bytes0)

Rule argument

seq: ⊦ bytes ≠ [] → (bytes + bytes0).first = bytes.first subst: [bytes0, bytes] → [by ', bytes0.rest] rotate: F spec: list inst: bytelist name: first-01

Additional information

Used terms: by ', bytes0.rest