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Proof step 2 from proof sgn-last-same (previous step)

⊦ sgn(bits + boolvar ') = boolvar ', (¬ boolvar) ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ false ∈ bits ∧ bits ≠ [] → sgn(bits) = true '
Proof step 4:
¬(¬ false ∈ bits + boolvar ' ∧ bits + boolvar ' ≠ []) ⊦ sgn(bits + boolvar ') = boolvar ', (¬ boolvar) ∈ bits

Rule argument

name: sgn-true rotate: F subst: [bits] → [bits + boolvar ']

Additional information

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