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Proof step 19 from proof bytes2int-mone (previous step)

b2i(by) < 0 ⊦ bits2int(true ' + byte2bits(by) + bytes2bits(bytes)) = bits2int(byte2bits(by) + bytes2bits(bytes)), (byte2bits(by) + bytes2bits(bytes)).first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first)

Rule argument

seq: ⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first) subst: [bits0, bits] → [bytes2bits(bytes), byte2bits(by)] rotate: F spec: list inst: bitlista name: first-01

Additional information

Used simplifier rules: byte2bits-empty: ⊦ byte2bits(by) ≠ [];%byte2bits-empty: ⊦ byte2bits(by) ≠ [];%byte2bits-first: ⊦ byte2bits(by).first ↔ b2i(by) < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: bytes2bits(bytes), byte2bits(by)