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Proof step 4 from proof bitsand-zeros-01 (previous step)

1 + # bits1 < # bits ⊦ bits = [], bitsand(bits, false ' + bits1) = false ' + mklist(false, # bits1), true ∈ bits

User applied rule induction

And obtained the following new goals

Proof step 5:
1 + # bits1 < # bits, ∀ bits1, bits0. # bits0 < # bits → 1 + # bits1 < # bits0 → bits0 = [] ∨ bitsand(bits0, false ' + bits1) = false ' + mklist(false, # bits1) ∨ true ∈ bits0 ⊦ bits = [] ∨ bitsand(bits, false ' + bits1) = false ' + mklist(false, # bits1) ∨ true ∈ bits

Rule argument

indvar: # bits wfpred: <

Additional information

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