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Proof step 57 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((byte2bits(by) + byte2bits(by0) + bytes2bits(bytes0)) + byte2bits(by1))) = by ' + by0 ' + bytes0 + by1 ', (true ∈ byte2bits(by) ∨ true ∈ byte2bits(by0) ∨ true ∈ bytes2bits(bytes0)) ∧ (false ∈ byte2bits(by) ∨ false ∈ byte2bits(by0) ∨ false ∈ bytes2bits(bytes0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 58:
⊦ byte2bits(by) = fillsgn(8, int2bits(b2i(by)))
Proof step 59:
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((fillsgn(8, int2bits(b2i(by))) + byte2bits(by0) + bytes2bits(bytes0)) + byte2bits(by1))) = by ' + by0 ' + bytes0 + by1 ', (true ∈ fillsgn(8, int2bits(b2i(by))) ∨ true ∈ byte2bits(by0) ∨ true ∈ bytes2bits(bytes0)) ∧ (false ∈ fillsgn(8, int2bits(b2i(by))) ∨ false ∈ byte2bits(by0) ∨ false ∈ bytes2bits(bytes0))

Rule argument

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

Additional information

Used terms: by