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Proof step 15 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) ⊦ bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ ¬ bits.first ∧ bits ≠ [] → uint2bits(bits2uint(bits)) = sgn(bits)
Proof step 17:
¬(¬ bitsinvert(bits) +1.first ∧ bitsinvert(bits) +1 ≠ []), 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) ⊦ bits = []
Proof step 23:
¬ bitsinvert(bits) +1.first ∧ bitsinvert(bits) +1 ≠ [], bits.first, 0 < bits2uint(bitsinvert(bits) +1), 2 ^ n→i(# bits) < bits2uint(bitsinvert(bits) +1), 2 + # bits ≤ # sgn(bitsinvert(bits) +1), 0 ≤ bits2uint(bitsinvert(bits) +1) ⊦ bits = []

Rule argument

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

Additional information

Used terms: bitsinvert(bits) +1