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Proof step 4 from proof sgn-append-06 (previous step)

(¬ boolvar) ∈ bits ⊦ sgn(bits + boolvar ' + bits1) = sgn(bits) + boolvar ' + bits1

User applied rule insert lemma

And obtained the following new goals

Proof step 5:
⊦ true ∈ bits ∧ false ∈ bits → sgn(bits + bits0) = sgn(bits) + bits0
Proof step 6:
true ∈ bits + boolvar ' ∧ false ∈ bits + boolvar ' → sgn((bits + boolvar ') + bits1) = sgn(bits + boolvar ') + bits1, (¬ boolvar) ∈ bits ⊦ sgn(bits + boolvar ' + bits1) = sgn(bits) + boolvar ' + bits1

Rule argument

name: sgn-append-01 subst: [bits, bits0] → [bits + boolvar ', bits1]

Additional information

Used terms: bits + boolvar ', bits1