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Proof step 12 from proof bits2int-nls (previous step)

bits2int(bits) < 0, 2 ^ n→i(# bits) + bits2int(bits) < 0, 2 + # bits ≤ # uint2bits(~ bits2int(bits)), bits2int(bits) ≤ 0 ⊦ bits = [], bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ bits.first ∧ bits ≠ [] → bits2int(bits) = ~ bits2uint(bitsinvert(bits) +1)
Proof step 14:
bits.first ∧ bits ≠ [], ~ bits2uint(bitsinvert(bits) +1) < 0, 2 ^ n→i(# bits) + ~ bits2uint(bitsinvert(bits) +1) < 0, 2 + # bits ≤ # uint2bits(~ ~ bits2uint(bitsinvert(bits) +1)), ~ bits2uint(bitsinvert(bits) +1) ≤ 0 ⊦ bits = [], bits = []

Rule argument

name: bits2int-neg-03 rotate: F subst: [bits] → [bits]

Additional information

Used simplifier rules: bits2int-first-01: bits ≠ [] ⊦ bits2int(bits) < 0 → bits.first; Used terms: bits