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Proof step 3 from proof add-ones-lelen (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsand(bits, bits0) = bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last)
Proof step 5:
¬(1 < # bits ∧ 1 < # bits0), # bits ≤ # bits0, ∀ bits1, bits. # bits1 < # bits0 → true → ¬ false ∈ bits ∧ # bits ≤ # bits1 ∧ bits ≠ [] → bitsand(bits, bits1) = bits1 ⊦ bits = [], bitsand(bits, bits0) = bits0, false ∈ bits
Proof step 9:
1 < # bits ∧ 1 < # bits0, # bits ≤ # bits0, ∀ bits1, bits. # bits1 < # bits0 → true → ¬ false ∈ bits ∧ # bits ≤ # bits1 ∧ bits ≠ [] → bitsand(bits, bits1) = bits1 ⊦ bits = [], bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last) = bits0, false ∈ bits

Rule argument

name: and-rec rotate: F subst: [bits0, bits] → [bits0, bits]

Additional information

Used terms: bits0, bits