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Proof step 11 from proof sgn-one-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
sgn(false ' + bits0) = true ', bits0.first, false ∈ bits0 ⊦ bits0 = [], sgn(bits0) = true '

Rule argument

Additional information

Used simplifier rules: sgn-one: ⊦ sgn(boolvar ') = boolvar ';%sgn-base-04: ⊦ ¬ boolvar ∈ bits → sgn(boolvar ' + bits) = boolvar ' + bits;% ⊦ boolvar ' = boolvar0 ' + bits ↔ (boolvar ↔ boolvar0) ∧ bits = [];% ⊦ boolvar ' = boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + [] = bits;