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Proof step 2 from proof and-size-one (previous step)

# bits ≤ # bits1, bits.first ⊦ bits = [], bitsand(bits, bits0 + bits1) = bits0 + bitsand(bits, bits1)

User applied rule induction

And obtained the following new goals

Proof step 3:
# bits ≤ # bits1 ∧ bits.first, ∀ bits2, bits1, bits0. # bits2 < # bits → # bits2 ≤ # bits1 ∧ bits2.first → bits2 = [] ∨ bitsand(bits2, bits0 + bits1) = bits0 + bitsand(bits2, bits1) ⊦ bits = [] ∨ bitsand(bits, bits0 + bits1) = bits0 + bitsand(bits, bits1)

Rule argument

indvar: # bits wfpred: <

Additional information

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