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Proof step 1 from proof sgn-last (conclusion)

(¬ boolvar) ∈ bits ⊦ sgn(boolvar ' + bits + boolvar0 ') = sgn(boolvar ' + bits) + boolvar0 '

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ boolvar, boolvar0. (¬ boolvar) ∈ bits0 → sgn(boolvar ' + bits0 + boolvar0 ') = sgn(boolvar ' + bits0) + boolvar0 ' ⊦ (¬ boolvar1) ∈ boolvar + bits0 → sgn(boolvar1 ' + (boolvar + bits0) + boolvar0 ') = sgn(boolvar1 ' + (boolvar + bits0)) + 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;% ⊦ bits + [] = bits;% ⊦ ¬ boolvar ∈ [];