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Proof step 1 from proof sgn-first-02 (conclusion)

⊦ sgn(true ' + bits) ≠ false ' + bits0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
sgn(true ' + bits) = false ' + bits0, false ∈ bits ⊦

Rule argument

Additional information

Used simplifier rules: sgn-in-02: ⊦ boolvar ∈ sgn(boolvar0 ' + bits) ↔ boolvar ∈ boolvar0 ' + bits;% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)