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Proof step 2 from proof bitsxor-is-orand (previous step)

⊦ bits = [], bits0 = [], bits2int(bitsxor(bits, bits0)) = bits2int(bitsor(bitsand(bitsinvert(bits), bits0), bitsand(bitsinvert(bits0), bits)))

User applied rule induction

And obtained the following new goals

Proof step 3:
true, ∀ bits, bits1. # bits1 < # bits0 → true → bits = [] ∨ bits1 = [] ∨ bits2int(bitsxor(bits, bits1)) = bits2int(bitsor(bitsand(bitsinvert(bits), bits1), bitsand(bitsinvert(bits1), bits))) ⊦ bits = [] ∨ bits0 = [] ∨ bits2int(bitsxor(bits, bits0)) = bits2int(bitsor(bitsand(bitsinvert(bits), bits0), bitsand(bitsinvert(bits0), bits)))

Rule argument

indvar: # bits0 wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: # bits0