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Proof step 2 from proof sgn-append-03 (previous step)

⊦ bits = [], sgn(bits + bits0) = sgn((¬ boolvar)' + bits0), boolvar ∈ bits

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ bits1, boolvar. bits0 = [] ∨ sgn(bits0 + bits1) = sgn((¬ boolvar)' + bits1) ∨ boolvar ∈ bits0 ⊦ boolvar + bits0 = [] ∨ sgn((boolvar + bits0) + bits1) = sgn((¬ boolvar0)' + bits1) ∨ boolvar0 ∈ boolvar + bits0

Rule argument

indvar: bits

Additional information

Used simplifier rules: bitlist freely generated by [], +;;