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Proof step 7 from proof sgn-append-06 (previous step)

(¬ boolvar) ∈ bits ⊦ true ∈ bits + boolvar ' ∧ false ∈ bits + boolvar ', sgn(bits + boolvar ' + bits1) = sgn(bits) + boolvar ' + bits1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
(¬ boolvar) ∈ bits ⊦ sgn(bits + boolvar ' + bits1) = sgn(bits) + boolvar ' + bits1, (boolvar ∨ true ∈ bits) ∧ (¬ boolvar ∨ false ∈ bits)

Rule argument

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);