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Proof step 1 from proof sgn-first (conclusion)

⊦ sgn(boolvar ' + bits).first ↔ boolvar

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ boolvar. sgn(boolvar ' + bits0).first ↔ boolvar ⊦ sgn(boolvar0 ' + (boolvar + bits0)).first ↔ boolvar0

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 '.first ↔ boolvar;