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Proof step 2 from proof sgn-notsame-01 (previous step)

sgn(bits) = boolvar ' + boolvar ' + bits0 ⊦

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ boolvar, bits1. sgn(bits0) ≠ boolvar ' + boolvar ' + bits1 ⊦ sgn(boolvar + bits0) ≠ boolvar0 ' + boolvar0 ' + bits1

Rule argument

indvar: bits

Additional information

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