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# 15-815 Automated Theorem Proving

# Lecture 31: Residuating Equational Constraints

After finishing the proof of cut elimination which heavily
relies on the completeness of regular derivations, we residuate
equational constraints. This is similar to the same process
for the logic without equality, except that now implicational formulas
may arises in the residuated constraints. The corresponding
problem is called *simultaneous rigid E-unification*.

### Reading

- Pages 115-116 of Handout 16 on
*Equality* (also availabe in
PDF format).

### Key Concepts

- Admissibility of cut
- Rigid equational constraints
- Simultaneous rigid E-unification

### Links

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Frank Pfenning
fp@cs