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Proof step 4 from proof bytes2int-pos (previous step)

⊦ 0 ≤ bits2int(bytes2bits(bytes)) ↔ bytes = [] ∨ ¬ b2i(bytes.first) < 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ bits ≠ [] → (0 ≤ bits2int(bits) ↔ ¬ bits.first)
Proof step 6:
bytes2bits(bytes) ≠ [] ⊦ ¬ bytes2bits(bytes).first ↔ bytes = [] ∨ ¬ b2i(bytes.first) < 0

Rule argument

seq: ⊦ bits ≠ [] → (0 ≤ bits2int(bits) ↔ ¬ bits.first) subst: [bits] → [bytes2bits(bytes)] rotate: F spec: int2bits inst: name: bits2int-ge-zero

Additional information

Used simplifier rules: bytes2bits-empty-01: ⊦ bytes2bits(bytes) = [] ↔ bytes = [];%bytes2bits-empty: ⊦ bytes2bits([]) = [];% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ bits2int([]) = 0; Used terms: bytes2bits(bytes)