dedekind-reals

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A formalization of the Dedekind real numbers in Coq.

The formalization started as a student project at the University of Ljubljana. At this point the formalization of the field of reals is finished.

There are still several unfinished theorems concering the lattice-theoretic structure of the reals (search for todo in the Coq files). We would be delighted by contributions that would bring the formalization closer to completion.

Compilation instruction

A fairly recent version of Coq should do. Run make to compile the files:

• make -- to compile
• make all -- to make all that is to be made
• make clean -- to remove the compiled files
• make html -- to make the HTML documentation
• make install -- installs files as the library DedekindReals

Structure of the modules

• MiscLemmas: various lemmas about rational numbers
• Cut: definition of Dedekind cuts and several other basic notions
• Additive: Additive structure of the reals
• Multiplication : Multiplicative structure of the relas
• Order : The order on the reals
• Archimedean: the proof that the reals satisfy the archimedean property
• Completeness: the reals are Dedekind-complete