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Proof step 45 from proof bytes2bytes-other (previous step)

∀ bytes1. # bytes1 < #((by0 + bytes) + by ') → bytes2bits(bytes1) ≠ [] → bytes1 = [] ∨ b2i(bytes1.first) = 0 ∨ b2i(bytes1.first) = ~1 ∨ bits2bytes(sgn(bytes2bits(bytes1))) = bytes1 ⊦ b2i(by0) = ~1, b2i(by0) = 0, bits2bytes(sgn(byte2bits(by0) + bytes2bits(bytes))) + i2b(bits2int(lastn(8, sgn(byte2bits(by0) + bytes2bits(bytes)) + byte2bits(by)))) ' = (by0 ' + bytes) + by ', ¬ false ∈ byte2bits(by0) ∧ ¬ false ∈ bytes2bits(bytes), ¬ true ∈ byte2bits(by0) ∧ ¬ true ∈ bytes2bits(bytes)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ n = # bits → lastn(n, bits0 + bits) = bits
Proof step 47:
8 = # byte2bits(by), ∀ bytes1. # bytes1 < #((by0 + bytes) + by ') → bytes2bits(bytes1) ≠ [] → bytes1 = [] ∨ b2i(bytes1.first) = 0 ∨ b2i(bytes1.first) = ~1 ∨ bits2bytes(sgn(bytes2bits(bytes1))) = bytes1 ⊦ b2i(by0) = ~1, b2i(by0) = 0, bits2bytes(sgn(byte2bits(by0) + bytes2bits(bytes))) + i2b(bits2int(byte2bits(by))) ' = (by0 ' + bytes) + by ', ¬ false ∈ byte2bits(by0) ∧ ¬ false ∈ bytes2bits(bytes), ¬ true ∈ byte2bits(by0) ∧ ¬ true ∈ bytes2bits(bytes)

Rule argument

seq: ⊦ n = # bits → lastn(n, bits0 + bits) = bits subst: [bits, bits0, n] → [byte2bits(by), sgn(byte2bits(by0) + bytes2bits(bytes)), 8] rotate: F spec: list-del inst: bitlista name: lastN-append

Additional information

Used simplifier rules: byte2bits-length: ⊦ # byte2bits(by) = 8; Used terms: byte2bits(by), sgn(byte2bits(by0) + bytes2bits(bytes)), 8