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Proof step 1 from proof add-ones-lelen (conclusion)

⊦ ¬ false ∈ bits ∧ # bits ≤ # bits0 ∧ bits ≠ [] → bitsand(bits, bits0) = bits0

User applied rule induction

And obtained the following new goals

Proof step 2:
true, ∀ bits1, bits. # bits1 < # bits0 → true → ¬ false ∈ bits ∧ # bits ≤ # bits1 ∧ bits ≠ [] → bitsand(bits, bits1) = bits1 ⊦ ¬ false ∈ bits ∧ # bits ≤ # bits0 ∧ bits ≠ [] → bitsand(bits, bits0) = bits0

Rule argument

indvar: # bits0 wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: # bits0