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Proof step 8 from proof ubits2bits (previous step)

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

User applied rule induction

And obtained the following new goals

Proof step 9:
bits.first, ∀ bits0. # bits0 < # bits → bits0.first → bits0 = [] ∨ 2 ^ n→i(# bits0) = bits2uint(bits0) + bits2uint(bitsinvert(bits0)) + 1 ⊦ bits = [] ∨ 2 ^ n→i(# bits) = bits2uint(bits) + bits2uint(bitsinvert(bits)) + 1

Rule argument

indvar: # bits wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: # bits