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Proof step 24 from proof bits2int-nls (previous step)

0 ≤ bits2uint(bitsinvert(bits) +1), 2 + # bits ≤ # sgn(bitsinvert(bits) +1), 2 ^ n→i(# bits) < bits2uint(bitsinvert(bits) +1), 0 < bits2uint(bitsinvert(bits) +1), bits.first ⊦ bitsinvert(bits) +1 = [], bits = [], bitsinvert(bits) +1.first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ # bits ≤ n + 1 → ¬ 2 + n ≤ # sgn(bits)

Rule argument

seq: ⊦ # bits ≤ n + 1 → ¬ 2 + n ≤ # sgn(bits) subst: [bits, n] → [bitsinvert(bits) +1, # bits] rotate: F spec: bitopsaux inst: name: sgn-length-03

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ ¬ # bits + 1 < # bitsinvert(bits) +1;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: bitsinvert(bits) +1, # bits