Commit 2ca7cc90 authored by Lawrence Paulson's avatar Lawrence Paulson
Browse files

tidying of IsaGeoCoq including a shorter abstract and revised title

parent a73264d7944f
......@@ -2024,57 +2024,35 @@ abstract =
notify = tjm1983@gmail.com
 
[IsaGeoCoq]
title = Tarski's postulate of parallels implies the 5th postulate of Euclid, the postulate of Playfair and the original postulate of Euclid.
title = Tarski's Parallel Postulate implies the 5th Postulate of Euclid, the Postulate of Playfair and the original Parallel Postulate of Euclid
author = Roland Coghetto <mailto:roland_coghetto@hotmail.com>
topic = Mathematics/Geometry
license = LGPL
date = 2021-01-31
notify = roland_coghetto@hotmail.com
abstract =
The GeoCoq library (Main autors: Michael Beeson, Pierre Boutry,
Gabriel Braun, Charly Gries, Julien Narboux) contains a formalization
The <a href="https://geocoq.github.io/GeoCoq/">GeoCoq library</a> contains a formalization
of geometry using the Coq proof assistant. It contains both proofs
about the foundations of geometry and high-level proofs in the same
style as in high-school. Some theorems also inspired by W.
Schwabhaüser, W. Szmielew and A. Tarski are also formalized with
others ITP (Metamath, Mizar) or ATP. We port a part of the GeoCoq
2.4.0 library within the Isabelle/Hol proof assistant: more precisely,
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. While the demonstrations in Coq are written in
procedural language, the transcript is done in declarative language
Isar. The synthetic approach of the demonstrations are directly
inspired by those contained in GeoCoq. Some demonstrations are
credited to G.E Martin(<<lemma bet_le__lt:>> in
Ch11_angles.thy, proved by Martin as Theorem 18.17) or Gupta H.N
(Krippen Lemma, proved by Gupta in its PhD in 1965 as Theorem 3.45).
In this work, the proofs are not contructive. The sledeghammer tool
being used to find some demonstrations. The names of the lemmas and
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.
A different translation has been proposed when the name was already
used in Isabel/Hol ("Len" is translated as
"TarskiLen") or that characters were not allowed in
Isabel/Hol ("anga'" in Ch13_angles.v is translated as
"angaP"). For some definitions the highlighting of a
variable has changed the order or the position of the variables
(Midpoint, Out, Inter,...). All the lemmas are valid in
absolute/neutral space defined with Tarski's axioms. It should
be noted that T.J.M. Makarios \cite{afp-Tarskis_Geometry} has begun
some demonstrations of certain proposals mainly those corresponding to
SST chapters 2 and 3. It uses a definition that does not quite
coincide with the definition used in Geocoq and here. As an example,
Makarios introduces the axiom A11 (Axiom of continuity) in the
definition of the locale "Tarski_absolute_space".
Furthermore, the definition of the locale "TarskiAbsolute"
\cite{afp-Poincare_Disc} is not not identical to the one defined in
the "Tarski_neutral_dimensionless" class of GeoCoq. Indeed
this one does not contain the axiom "upper_dimension". In
some cases particular, it is nevertheless to use the axiom
"upper_dimension". The addition of the word "_2D"
in the file indicates its presence. In the last part, it is
It should be noted that T.J.M. Makarios has done
<a href="https://www.isa-afp.org/entries/Tarskis_Geometry.html">some proofs in Tarski's Geometry</a>. It uses a definition that does not quite
coincide with the definition used in Geocoq and here.
Furthermore, corresponding definitions in the <a href="https://www.isa-afp.org/entries/Poincare_Disc.html">Poincaré Disc Model
development</a>
are not 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 the system of Tarski implies the Playfair axiom, the 5th
postulate of euclide and the postulate original from Euclid. These
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.
 
......
......@@ -2,7 +2,7 @@
<html lang="en">
<head>
<meta charset="utf-8">
<title>Tarski's postulate of parallels implies the 5th postulate of Euclid, the postulate of Playfair and the original postulate of Euclid. - Archive of Formal Proofs
<title>Tarski's Parallel Postulate implies the 5th Postulate of Euclid, the Postulate of Playfair and the original Parallel Postulate of Euclid - Archive of Formal Proofs
</title>
<link rel="stylesheet" type="text/css" href="../front.css">
<link rel="icon" href="../images/favicon.ico" type="image/icon">
......@@ -76,11 +76,9 @@ MathJax = {
<p>&nbsp;</p>
<h1> <font class="first">T</font>arski's
postulate
<font class="first">P</font>arallel
of
parallels
<font class="first">P</font>ostulate
implies
......@@ -88,7 +86,7 @@ MathJax = {
<font class="first">5</font>th
postulate
<font class="first">P</font>ostulate
of
......@@ -96,7 +94,7 @@ MathJax = {
the
postulate
<font class="first">P</font>ostulate
of
......@@ -108,11 +106,13 @@ MathJax = {
original
postulate
<font class="first">P</font>arallel
<font class="first">P</font>ostulate
of
<font class="first">E</font>uclid.
<font class="first">E</font>uclid
</h1>
<p>&nbsp;</p>
......@@ -121,7 +121,7 @@ MathJax = {
<tbody>
<tr>
<td class="datahead" width="20%">Title:</td>
<td class="data" width="80%">Tarski's postulate of parallels implies the 5th postulate of Euclid, the postulate of Playfair and the original postulate of Euclid.</td>
<td class="data" width="80%">Tarski's Parallel Postulate implies the 5th Postulate of Euclid, the Postulate of Playfair and the original Parallel Postulate of Euclid</td>
</tr>
<tr>
......@@ -143,50 +143,26 @@ MathJax = {
<tr>
<td class="datahead" valign="top">Abstract:</td>
<td class="abstract mathjax_process">
The GeoCoq library (Main autors: Michael Beeson, Pierre Boutry,
Gabriel Braun, Charly Gries, Julien Narboux) contains a formalization
The <a href="https://geocoq.github.io/GeoCoq/">GeoCoq library</a> contains a formalization
of geometry using the Coq proof assistant. It contains both proofs
about the foundations of geometry and high-level proofs in the same
style as in high-school. Some theorems also inspired by W.
Schwabhaüser, W. Szmielew and A. Tarski are also formalized with
others ITP (Metamath, Mizar) or ATP. We port a part of the GeoCoq
2.4.0 library within the Isabelle/Hol proof assistant: more precisely,
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. While the demonstrations in Coq are written in
procedural language, the transcript is done in declarative language
Isar. The synthetic approach of the demonstrations are directly
inspired by those contained in GeoCoq. Some demonstrations are
credited to G.E Martin(<<lemma bet_le__lt:>> in
Ch11_angles.thy, proved by Martin as Theorem 18.17) or Gupta H.N
(Krippen Lemma, proved by Gupta in its PhD in 1965 as Theorem 3.45).
In this work, the proofs are not contructive. The sledeghammer tool
being used to find some demonstrations. The names of the lemmas and
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.
A different translation has been proposed when the name was already
used in Isabel/Hol ("Len" is translated as
"TarskiLen") or that characters were not allowed in
Isabel/Hol ("anga'" in Ch13_angles.v is translated as
"angaP"). For some definitions the highlighting of a
variable has changed the order or the position of the variables
(Midpoint, Out, Inter,...). All the lemmas are valid in
absolute/neutral space defined with Tarski's axioms. It should
be noted that T.J.M. Makarios \cite{afp-Tarskis_Geometry} has begun
some demonstrations of certain proposals mainly those corresponding to
SST chapters 2 and 3. It uses a definition that does not quite
coincide with the definition used in Geocoq and here. As an example,
Makarios introduces the axiom A11 (Axiom of continuity) in the
definition of the locale "Tarski_absolute_space".
Furthermore, the definition of the locale "TarskiAbsolute"
\cite{afp-Poincare_Disc} is not not identical to the one defined in
the "Tarski_neutral_dimensionless" class of GeoCoq. Indeed
this one does not contain the axiom "upper_dimension". In
some cases particular, it is nevertheless to use the axiom
"upper_dimension". The addition of the word "_2D"
in the file indicates its presence. In the last part, it is
It should be noted that T.J.M. Makarios has done
<a href="https://www.isa-afp.org/entries/Tarskis_Geometry.html">some proofs in Tarski's Geometry</a>. It uses a definition that does not quite
coincide with the definition used in Geocoq and here.
Furthermore, corresponding definitions in the <a href="https://www.isa-afp.org/entries/Poincare_Disc.html">Poincaré Disc Model
development</a>
are not 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 the system of Tarski implies the Playfair axiom, the 5th
postulate of euclide and the postulate original from Euclid. These
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.</td>
</tr>
......@@ -197,7 +173,7 @@ Boutry, Charly Gries, Julien Narboux and Pascal Schreck.</td>
<td class="formatted">
<pre>@article{IsaGeoCoq-AFP,
author = {Roland Coghetto},
title = {Tarski's postulate of parallels implies the 5th postulate of Euclid, the postulate of Playfair and the original postulate of Euclid.},
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,
......
......@@ -90,7 +90,7 @@ of a scientific journal, is indexed by <a href="http://dblp.uni-trier.de/db/jour
</tr>
<tr>
<td class="entry">
2021-01-31: <a href="entries/IsaGeoCoq.html">Tarski's postulate of parallels implies the 5th postulate of Euclid, the postulate of Playfair and the original postulate of Euclid.</a>
2021-01-31: <a href="entries/IsaGeoCoq.html">Tarski's Parallel Postulate implies the 5th Postulate of Euclid, the Postulate of Playfair and the original Parallel Postulate of Euclid</a>
<br>
Author:
Roland Coghetto
......
......@@ -11,56 +11,32 @@
</description>
<pubDate>31 Jan 2021 00:00:00 +0000</pubDate>
<item>
<title>Tarski's postulate of parallels implies the 5th postulate of Euclid, the postulate of Playfair and the original postulate of Euclid.</title>
<title>Tarski's Parallel Postulate implies the 5th Postulate of Euclid, the Postulate of Playfair and the original Parallel Postulate of Euclid</title>
<link>https://www.isa-afp.org/entries/IsaGeoCoq.html</link>
<guid>https://www.isa-afp.org/entries/IsaGeoCoq.html</guid>
<dc:creator> Roland Coghetto </dc:creator>
<pubDate>31 Jan 2021 00:00:00 +0000</pubDate>
<description>
The GeoCoq library (Main autors: Michael Beeson, Pierre Boutry,
Gabriel Braun, Charly Gries, Julien Narboux) contains a formalization
The &lt;a href=&#34;https://geocoq.github.io/GeoCoq/&#34;&gt;GeoCoq library&lt;/a&gt; contains a formalization
of geometry using the Coq proof assistant. It contains both proofs
about the foundations of geometry and high-level proofs in the same
style as in high-school. Some theorems also inspired by W.
Schwabhaüser, W. Szmielew and A. Tarski are also formalized with
others ITP (Metamath, Mizar) or ATP. We port a part of the GeoCoq
2.4.0 library within the Isabelle/Hol proof assistant: more precisely,
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. While the demonstrations in Coq are written in
procedural language, the transcript is done in declarative language
Isar. The synthetic approach of the demonstrations are directly
inspired by those contained in GeoCoq. Some demonstrations are
credited to G.E Martin(&lt;&lt;lemma bet_le__lt:&gt;&gt; in
Ch11_angles.thy, proved by Martin as Theorem 18.17) or Gupta H.N
(Krippen Lemma, proved by Gupta in its PhD in 1965 as Theorem 3.45).
In this work, the proofs are not contructive. The sledeghammer tool
being used to find some demonstrations. The names of the lemmas and
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.
A different translation has been proposed when the name was already
used in Isabel/Hol (&#34;Len&#34; is translated as
&#34;TarskiLen&#34;) or that characters were not allowed in
Isabel/Hol (&#34;anga&#39;&#34; in Ch13_angles.v is translated as
&#34;angaP&#34;). For some definitions the highlighting of a
variable has changed the order or the position of the variables
(Midpoint, Out, Inter,...). All the lemmas are valid in
absolute/neutral space defined with Tarski&#39;s axioms. It should
be noted that T.J.M. Makarios \cite{afp-Tarskis_Geometry} has begun
some demonstrations of certain proposals mainly those corresponding to
SST chapters 2 and 3. It uses a definition that does not quite
coincide with the definition used in Geocoq and here. As an example,
Makarios introduces the axiom A11 (Axiom of continuity) in the
definition of the locale &#34;Tarski_absolute_space&#34;.
Furthermore, the definition of the locale &#34;TarskiAbsolute&#34;
\cite{afp-Poincare_Disc} is not not identical to the one defined in
the &#34;Tarski_neutral_dimensionless&#34; class of GeoCoq. Indeed
this one does not contain the axiom &#34;upper_dimension&#34;. In
some cases particular, it is nevertheless to use the axiom
&#34;upper_dimension&#34;. The addition of the word &#34;_2D&#34;
in the file indicates its presence. In the last part, it is
It should be noted that T.J.M. Makarios has done
&lt;a href=&#34;https://www.isa-afp.org/entries/Tarskis_Geometry.html&#34;&gt;some proofs in Tarski&#39;s Geometry&lt;/a&gt;. It uses a definition that does not quite
coincide with the definition used in Geocoq and here.
Furthermore, corresponding definitions in the &lt;a href=&#34;https://www.isa-afp.org/entries/Poincare_Disc.html&#34;&gt;Poincaré Disc Model
development&lt;/a&gt;
are not 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 the system of Tarski implies the Playfair axiom, the 5th
postulate of euclide and the postulate original from Euclid. These
parallels of Tarski&#39;s system implies the Playfair axiom, the 5th
postulate of Euclid and Euclid&#39;s original parallel postulate. These
proofs, which are not constructive, are directly inspired by Pierre
Boutry, Charly Gries, Julien Narboux and Pascal Schreck.</description>
</item>
......
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment