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Proof step 2 from proof sgn-in (previous step)

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

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: bits

Additional information

Used simplifier rules: sgn-one: ⊦ sgn(boolvar ') = boolvar ';%bitlist freely generated by [], +;;% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' = boolvar0 ' ↔ boolvar ↔ boolvar0;