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Proof step 12 from proof sgn-last-same (previous step)

¬(¬ true ∈ bits + boolvar ' ∧ bits + boolvar ' ≠ []), false ∈ bits ⊦ sgn(bits + boolvar ') = boolvar ', (¬ boolvar) ∈ bits

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
false ∈ bits ⊦ sgn(bits + boolvar ') = boolvar ', (¬ boolvar) ∈ bits, ¬ boolvar ∧ ¬ true ∈ bits

Rule argument

Additional information

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