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Proof step 2 from proof add-ones-grlen-02 (previous step)

# bits0 ≤ # bits ⊦ bits0 = [], bitsand(bits, bits0) = bits0, false ∈ bits, bits0.first

User applied rule induction

And obtained the following new goals

Proof step 3:
# bits0 ≤ # bits, ∀ bits, bits1. # bits1 < # bits0 → # bits1 ≤ # bits → bits1 = [] ∨ bitsand(bits, bits1) = bits1 ∨ false ∈ bits ∨ bits1.first ⊦ bits0 = [] ∨ bitsand(bits, bits0) = bits0 ∨ false ∈ bits ∨ bits0.first

Rule argument

indvar: # bits0 wfpred: <

Additional information

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