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# 15-815 Automated Theorem Proving

# Lecture 30: Cut Elimination with Equality

We finish the proof that *regular derivations*
are complete for the sequent calculus with equality and then
prove the cut elimination theorem for regular derivations.

The resulting system can be reformulated by residuating
equality constraints, except that these equality constraints
now may depend on equational assumptions. Theorem proving
in this simple logic is called *rigid E-unification*.
We also discuss the more general problem of *E-unificaiton*.
Unfortunately, both problems are undecidable.

### Reading

- Pages 111-114 of Handout 16
on
*Equality* (also availabe in
PDF format).

### Key Concepts

- Equational derivations
- Regular derivations
- Cut elimination with equality

### Links

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Frank Pfenning
fp@cs