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Proof step 1 from proof and-notone-02 (conclusion)

⊦ bits ≠ [] → bitsand(bits, false ' + bits0) + bits2 ≠ true ' + bits1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
bitsand(bits, false ' + bits0) + bits2 = true ' + bits1 ⊦ bits = [], ¬ true ∈ bitsand(bits, false ' + bits0) ∧ ¬ true ∈ bits2

Rule argument

Additional information

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