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Proof step 18 from proof bits2int-nls (previous step)

bits.first, 0 < bits2uint(bitsinvert(bits) +1), 2 ^ n→i(# bits) < bits2uint(bitsinvert(bits) +1), 2 + # bits ≤ # uint2bits(bits2uint(bitsinvert(bits) +1)), 0 ≤ bits2uint(bitsinvert(bits) +1), bitsinvert(bits) +1.first ⊦ bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ bits.first ∧ bits ≠ [] → uint2bits(bits2uint(bits)) = false ' + bits
Proof step 20:
bitsinvert(bits) +1.first ∧ bitsinvert(bits) +1 ≠ [], bits.first, 0 < bits2uint(bitsinvert(bits) +1), 2 ^ n→i(# bits) < bits2uint(bitsinvert(bits) +1), 2 + # bits ≤ #(false ' + bitsinvert(bits) +1), 0 ≤ bits2uint(bitsinvert(bits) +1), bitsinvert(bits) +1.first ⊦ bits = []

Rule argument

name: ubits2ubits-neg rotate: F subst: [bits] → [bitsinvert(bits) +1]

Additional information

Used simplifier rules: ⊦ ¬ bits +1 ≠ [] ↔ false; Used terms: bitsinvert(bits) +1