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Proof step 1 from proof bitsand-first-samesize (conclusion)

⊦ # bits = # bits0 ∧ 1 < # bits → bitsand(bits, bits0) = (bits.first ∧ bits0.first)' + bitsand(bits.rest, bits0.rest)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
# bits = # bits0 ⊦ bitsand(bits, bits0) = (bits.first ∧ bits0.first)' + bitsand(bits.rest, bits0.rest), # bits0 = 1, bits = []

Rule argument

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = [];% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);