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Proof step 23 from proof sgn-one-01 (previous step)

sgn(boolvar ' + bits0) = false ', sgn(bits0) = false ' ∧ true ∈ bits0 → bits0 = [] ⊦ bits0 ≠ [] ∧ (bits0.first ↔ boolvar), ¬ true ∈ bits0 ∧ ¬ boolvar

User applied rule case distinction

And obtained the following new goals

Proof step 24:
sgn(boolvar ' + bits0) = false ', sgn(bits0) = false ' ∧ true ∈ bits0 → bits0 = [] ⊦ bits0.first ↔ boolvar, ¬ true ∈ bits0 ∧ ¬ boolvar

Rule argument

pos: right 1

Additional information

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