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Proof step 4 from proof sgn-base-04 (previous step)

¬(bits ≠ [] ∧ (bits.first ↔ ¬ boolvar)) ⊦ sgn(boolvar ' + bits) = boolvar ' + bits, boolvar ∈ bits

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ sgn(boolvar ' + bits) = boolvar ' + bits, bits.first ↔ ¬ boolvar, bits = [], boolvar ∈ bits

Rule argument

Additional information

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