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 completeion.
Compilation instruction
A fairly recent version of Coq should do. Run make
to compile the files:
make
-- to compilemake all
-- to make all that is to be mademake clean
-- to remove the compiled filesmake html
-- to make the HTML documentationmake install
-- we have never tried to run this
Structure of the modules
MiscLemmas
: various lemmas about rational numbersCut
: definition of Dedekind cuts and several other basic notionsAdditive
: Additive structure of the realsMultiplication
: Multiplicative structure of the relasOrder
: The order on the realsArchimedean
: the proof that the reals satisfy the archimedean propertyCompleteness
: the reals are Dedekind-complete