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Proof step 2 from proof sgn-length-03 (previous step)

# bits ≤ n + 1, 2 + n ≤ # sgn(bits) ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ # bits < # sgn(bits)

Rule argument

name: sgn-length subst: [bits] → [bits]

Additional information

Used simplifier rules: ⊦ ¬ m < n ↔ n ≤ m;% ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward)%n0 < n ⊦ m + (* n) ≤ m0 + (* n0) ↔ m + (n - n0) ≤ m0;% ⊦ m + n ≤ m ↔ n = 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: bits