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Proof step 7 from proof bits2uint-inv-neg (previous step)

∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ 2 ^ n→i(# bits0) = bits2uint(bitsinvert(bits0)) + bits2uint(bits0) + 1 ∨ bits0.first ⊦ 2 ^ n→i(# bits) = bits2uint(bitsinvert(bits)) + bits2uint(bits) + 1, bits = [], bits.first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ bits ≠ [] ∧ ¬ bits.last → bits2uint(bits) = bits2uint(bits.butlast) * 2
Proof step 9:
¬(bits ≠ [] ∧ ¬ bits.last), ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ 2 ^ n→i(# bits0) = bits2uint(bitsinvert(bits0)) + bits2uint(bits0) + 1 ∨ bits0.first ⊦ 2 ^ n→i(# bits) = bits2uint(bitsinvert(bits)) + bits2uint(bits) + 1, bits = [], bits.first
Proof step 16:
bits ≠ [] ∧ ¬ bits.last, ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ 2 ^ n→i(# bits0) = bits2uint(bitsinvert(bits0)) + bits2uint(bits0) + 1 ∨ bits0.first ⊦ 2 ^ n→i(# bits) = bits2uint(bitsinvert(bits)) + bits2uint(bits.butlast) * 2 + 1, bits = [], bits.first

Rule argument

name: bits2uint-rec-01 rotate: F subst: [bits] → [bits]

Additional information

Used terms: bits