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Proof step 67 from proof bitsand-cast-01 (previous step)

# bits1 = # bitsand(bits, bits1), # bits1 = # bitsand(bits1, bits), # bits = # bits1 ⊦ bits1 = [], bits2 + bits1 = [], bits2 = [], bits3 + bits = [], bits3 = [], bitsand(bits, bits1) = bitsand(bits1, bits), bits1.first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 68:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)

Rule argument

name: and-com rotate: F subst: [bits0, bits] → [bits, bits1]

Additional information

Used simplifier rules: ⊦ # [] = 0;% ⊦ # bits = 0 ↔ bits = []; Used terms: bits, bits1