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# 15-815 Automated Theorem Proving

# Lecture 25: Lifting Lemma

Following the propositional case, it is straightforward to prove that even
in the first-order case, the forward sequent calculus is sound and complete
with respect to the backward sequent calculus, and that it satisfies a strong
subformula property. The completeness property is usually called
*ground completeness*.

It is more difficult to see that working with schematic sequents and
calculating most general unifiers preserves this completeness. The
necessity for factoring shows that there are some subtleties. The
lemma which shows that ground completeness implies completeness
with schematic sequents is called a *lifting lemma*. We sketch
the necessary definitions and proof of the lifting lemma.

### Reading

*none yet*
### Key Concepts

- Resolution
- Ground completeness
- Lifting lemma

### Links

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Frank Pfenning
fp@cs