### Abstract

This theory contains a formalization of decreasing diagrams showing that any locally decreasing abstract rewrite system is confluent. We consider the valley (van Oostrom, TCS 1994) and the conversion version (van Oostrom, RTA 2008) and closely follow the original proofs. As an application we prove Newman's lemma.

### License

GNU Lesser General Public License (LGPL)

### Topics

- Logic/Rewriting

### Session Decreasing-Diagrams

- Decreasing_Diagrams

### Depends on

- Abstract Rewriting

### Auto-related entries

- Decreasing Diagrams II
- Stewart’s Theorem and Apollonius' Theorem
- The Z Property

## Cite

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Decreasing-Diagrams-AFP

    @article{Decreasing-Diagrams-AFP,
      author  = {Harald Zankl},
      title   = {Decreasing Diagrams},
      journal = {Archive of Formal Proofs},
      month   = {November},
      year    = {2013},
      note    = {\url{https://isa-afp.org/entries/Decreasing-Diagrams.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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