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Proof step 22 from proof int2bytes-bytes2int-length-01 (previous step)

# sgn(bytes2bits(bytes)) = n * 8, # bytes < n ⊦ bytes = []

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 23:
⊦ ¬ # bits < # sgn(bits)

Rule argument

spec: bitopsaux inst: name: sgn-length seq: ⊦ ¬ # bits < # sgn(bits) subst: [bits] → [bytes2bits(bytes)] flags: []

Additional information

Used simplifier rules: bytes2bits-length: ⊦ # bytes2bits(bytes) = i→n(8) * # bytes;%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%le-num: 0 ≠ m ⊦ (* m) * n ≤ m * n0 ↔ n ≤ n0; from specification nat-mult%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: bytes2bits(bytes)