Abstract: 
The GeoCoq library contains a formalization
of geometry using the Coq proof assistant. It contains both proofs
about the foundations of geometry and highlevel proofs in the same
style as in high school. We port a part of the GeoCoq
2.4.0 library to Isabelle/HOL: more precisely,
the files Chap02.v to Chap13_3.v, suma.v as well as the associated
definitions and some useful files for the demonstration of certain
parallel postulates. The synthetic approach of the demonstrations is directly
inspired by those contained in GeoCoq. The names of the lemmas and
theorems used are kept as far as possible as well as the definitions.
It should be noted that T.J.M. Makarios has done
some proofs in Tarski's Geometry. It uses a definition that does not quite
coincide with the definition used in Geocoq and here.
Furthermore, corresponding definitions in the PoincarĂ© Disc Model
development are not identical to those defined in GeoCoq.
In the last part, it is
formalized that, in the neutral/absolute space, the axiom of the
parallels of Tarski's system implies the Playfair axiom, the 5th
postulate of Euclid and Euclid's original parallel postulate. These
proofs, which are not constructive, are directly inspired by Pierre
Boutry, Charly Gries, Julien Narboux and Pascal Schreck.

BibTeX: 
@article{IsaGeoCoqAFP,
author = {Roland Coghetto},
title = {Tarski's Parallel Postulate implies the 5th Postulate of Euclid, the Postulate of Playfair and the original Parallel Postulate of Euclid},
journal = {Archive of Formal Proofs},
month = jan,
year = 2021,
note = {\url{https://isaafp.org/entries/IsaGeoCoq.html},
Formal proof development},
ISSN = {2150914x},
}
