html export trial

2021-07-19 18:33:17 +01:00 · 2021-07-19 18:33:17 +01:00 · b930e449e3
commit b930e449e3
parent 5e06eeb654
6 changed files with 561 additions and 88 deletions
--- a/.markdown-preview.html
+++ b/.markdown-preview.html
@ -0,0 +1,41 @@
+<!DOCTYPE html>
+<html>
+  <head>
+    <meta charset="utf-8">
+    <meta name="viewport" content="width=device-width, initial-scale=1, minimal-ui">
+    <title>Markdown preview</title>
+    <link rel="stylesheet" type="text/css" href="https://thomasf.github.io/solarized-css/solarized-dark.min.css">
+    <script src="http://code.jquery.com/jquery-1.12.4.min.js"></script>
+    
+    <script>
+     (function($, undefined) {
+         var socket = new WebSocket("ws://localhost:7379");
+         socket.onopen = function() {
+             console.log("Connection established.");
+	     socket.send("MDPM-Register-UUID: 95ef6ea9-905f-406e-ab19-bc8a950fbadb");
+         };
+         socket.onclose = function(event) {
+             if (event.wasClean) {
+                 console.log('Connection closed gracefully.');
+             } else {
+                 console.log('Connection terminated.');
+             }
+             console.log('Code: ' + event.code + ' reason: ' + event.reason);
+         };
+         socket.onmessage = function(event) {
+             $("#markdown-body").html($(event.data).find("#content").html()).trigger('mdContentChange');
+             var scroll = $(document).height() * ($(event.data).find("#position-percentage").html() / 100);
+             $("html, body").animate({ scrollTop: scroll }, 600);
+         };
+         socket.onerror = function(error) {
+             console.log("Error: " + error.message);
+         };
+     })(jQuery);
+    </script>
+  </head>
+  <body>
+    <article id="markdown-body" class="markdown-body">
+      <p>Markdown preview</p>
+    </article>
+  </body>
+</html>
--- a/.projectile
+++ b/.projectile
--- a/HoTTGame.agda-lib
+++ b/HoTTGame.agda-lib
@ -0,0 +1,4 @@
+name: HoTTGameLib
+include: .
+depend: cubical-0.3
+flags: --cubical --no-import-sorts
--- a/Plan.html
+++ b/Plan.html
@ -0,0 +1,377 @@
+<?xml version="1.0" encoding="utf-8"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
+"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
+<head>
+<!-- 2021-07-19 Mon 18:31 -->
+<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
+<meta name="viewport" content="width=device-width, initial-scale=1" />
+<title>&lrm;</title>
+<meta name="author" content="JLH KL" />
+<meta name="generator" content="Org Mode" />
+<style type="text/css">
+ <!--/*--><![CDATA[/*><!--*/
+  .title  { text-align: center;
+             margin-bottom: .2em; }
+  .subtitle { text-align: center;
+              font-size: medium;
+              font-weight: bold;
+              margin-top:0; }
+  .todo   { font-family: monospace; color: red; }
+  .done   { font-family: monospace; color: green; }
+  .priority { font-family: monospace; color: orange; }
+  .tag    { background-color: #eee; font-family: monospace;
+            padding: 2px; font-size: 80%; font-weight: normal; }
+  .timestamp { color: #bebebe; }
+  .timestamp-kwd { color: #5f9ea0; }
+  .org-right  { margin-left: auto; margin-right: 0px;  text-align: right; }
+  .org-left   { margin-left: 0px;  margin-right: auto; text-align: left; }
+  .org-center { margin-left: auto; margin-right: auto; text-align: center; }
+  .underline { text-decoration: underline; }
+  #postamble p, #preamble p { font-size: 90%; margin: .2em; }
+  p.verse { margin-left: 3%; }
+  pre {
+    border: 1px solid #ccc;
+    box-shadow: 3px 3px 3px #eee;
+    padding: 8pt;
+    font-family: monospace;
+    overflow: auto;
+    margin: 1.2em;
+  }
+  pre.src {
+    position: relative;
+    overflow: auto;
+    padding-top: 1.2em;
+  }
+  pre.src:before {
+    display: none;
+    position: absolute;
+    background-color: white;
+    top: -10px;
+    right: 10px;
+    padding: 3px;
+    border: 1px solid black;
+  }
+  pre.src:hover:before { display: inline; margin-top: 14px;}
+  /* Languages per Org manual */
+  pre.src-asymptote:before { content: 'Asymptote'; }
+  pre.src-awk:before { content: 'Awk'; }
+  pre.src-C:before { content: 'C'; }
+  /* pre.src-C++ doesn't work in CSS */
+  pre.src-clojure:before { content: 'Clojure'; }
+  pre.src-css:before { content: 'CSS'; }
+  pre.src-D:before { content: 'D'; }
+  pre.src-ditaa:before { content: 'ditaa'; }
+  pre.src-dot:before { content: 'Graphviz'; }
+  pre.src-calc:before { content: 'Emacs Calc'; }
+  pre.src-emacs-lisp:before { content: 'Emacs Lisp'; }
+  pre.src-fortran:before { content: 'Fortran'; }
+  pre.src-gnuplot:before { content: 'gnuplot'; }
+  pre.src-haskell:before { content: 'Haskell'; }
+  pre.src-hledger:before { content: 'hledger'; }
+  pre.src-java:before { content: 'Java'; }
+  pre.src-js:before { content: 'Javascript'; }
+  pre.src-latex:before { content: 'LaTeX'; }
+  pre.src-ledger:before { content: 'Ledger'; }
+  pre.src-lisp:before { content: 'Lisp'; }
+  pre.src-lilypond:before { content: 'Lilypond'; }
+  pre.src-lua:before { content: 'Lua'; }
+  pre.src-matlab:before { content: 'MATLAB'; }
+  pre.src-mscgen:before { content: 'Mscgen'; }
+  pre.src-ocaml:before { content: 'Objective Caml'; }
+  pre.src-octave:before { content: 'Octave'; }
+  pre.src-org:before { content: 'Org mode'; }
+  pre.src-oz:before { content: 'OZ'; }
+  pre.src-plantuml:before { content: 'Plantuml'; }
+  pre.src-processing:before { content: 'Processing.js'; }
+  pre.src-python:before { content: 'Python'; }
+  pre.src-R:before { content: 'R'; }
+  pre.src-ruby:before { content: 'Ruby'; }
+  pre.src-sass:before { content: 'Sass'; }
+  pre.src-scheme:before { content: 'Scheme'; }
+  pre.src-screen:before { content: 'Gnu Screen'; }
+  pre.src-sed:before { content: 'Sed'; }
+  pre.src-sh:before { content: 'shell'; }
+  pre.src-sql:before { content: 'SQL'; }
+  pre.src-sqlite:before { content: 'SQLite'; }
+  /* additional languages in org.el's org-babel-load-languages alist */
+  pre.src-forth:before { content: 'Forth'; }
+  pre.src-io:before { content: 'IO'; }
+  pre.src-J:before { content: 'J'; }
+  pre.src-makefile:before { content: 'Makefile'; }
+  pre.src-maxima:before { content: 'Maxima'; }
+  pre.src-perl:before { content: 'Perl'; }
+  pre.src-picolisp:before { content: 'Pico Lisp'; }
+  pre.src-scala:before { content: 'Scala'; }
+  pre.src-shell:before { content: 'Shell Script'; }
+  pre.src-ebnf2ps:before { content: 'ebfn2ps'; }
+  /* additional language identifiers per "defun org-babel-execute"
+       in ob-*.el */
+  pre.src-cpp:before  { content: 'C++'; }
+  pre.src-abc:before  { content: 'ABC'; }
+  pre.src-coq:before  { content: 'Coq'; }
+  pre.src-groovy:before  { content: 'Groovy'; }
+  /* additional language identifiers from org-babel-shell-names in
+     ob-shell.el: ob-shell is the only babel language using a lambda to put
+     the execution function name together. */
+  pre.src-bash:before  { content: 'bash'; }
+  pre.src-csh:before  { content: 'csh'; }
+  pre.src-ash:before  { content: 'ash'; }
+  pre.src-dash:before  { content: 'dash'; }
+  pre.src-ksh:before  { content: 'ksh'; }
+  pre.src-mksh:before  { content: 'mksh'; }
+  pre.src-posh:before  { content: 'posh'; }
+  /* Additional Emacs modes also supported by the LaTeX listings package */
+  pre.src-ada:before { content: 'Ada'; }
+  pre.src-asm:before { content: 'Assembler'; }
+  pre.src-caml:before { content: 'Caml'; }
+  pre.src-delphi:before { content: 'Delphi'; }
+  pre.src-html:before { content: 'HTML'; }
+  pre.src-idl:before { content: 'IDL'; }
+  pre.src-mercury:before { content: 'Mercury'; }
+  pre.src-metapost:before { content: 'MetaPost'; }
+  pre.src-modula-2:before { content: 'Modula-2'; }
+  pre.src-pascal:before { content: 'Pascal'; }
+  pre.src-ps:before { content: 'PostScript'; }
+  pre.src-prolog:before { content: 'Prolog'; }
+  pre.src-simula:before { content: 'Simula'; }
+  pre.src-tcl:before { content: 'tcl'; }
+  pre.src-tex:before { content: 'TeX'; }
+  pre.src-plain-tex:before { content: 'Plain TeX'; }
+  pre.src-verilog:before { content: 'Verilog'; }
+  pre.src-vhdl:before { content: 'VHDL'; }
+  pre.src-xml:before { content: 'XML'; }
+  pre.src-nxml:before { content: 'XML'; }
+  /* add a generic configuration mode; LaTeX export needs an additional
+     (add-to-list 'org-latex-listings-langs '(conf " ")) in .emacs */
+  pre.src-conf:before { content: 'Configuration File'; }
+
+  table { border-collapse:collapse; }
+  caption.t-above { caption-side: top; }
+  caption.t-bottom { caption-side: bottom; }
+  td, th { vertical-align:top;  }
+  th.org-right  { text-align: center;  }
+  th.org-left   { text-align: center;   }
+  th.org-center { text-align: center; }
+  td.org-right  { text-align: right;  }
+  td.org-left   { text-align: left;   }
+  td.org-center { text-align: center; }
+  dt { font-weight: bold; }
+  .footpara { display: inline; }
+  .footdef  { margin-bottom: 1em; }
+  .figure { padding: 1em; }
+  .figure p { text-align: center; }
+  .equation-container {
+    display: table;
+    text-align: center;
+    width: 100%;
+  }
+  .equation {
+    vertical-align: middle;
+  }
+  .equation-label {
+    display: table-cell;
+    text-align: right;
+    vertical-align: middle;
+  }
+  .inlinetask {
+    padding: 10px;
+    border: 2px solid gray;
+    margin: 10px;
+    background: #ffffcc;
+  }
+  #org-div-home-and-up
+   { text-align: right; font-size: 70%; white-space: nowrap; }
+  textarea { overflow-x: auto; }
+  .linenr { font-size: smaller }
+  .code-highlighted { background-color: #ffff00; }
+  .org-info-js_info-navigation { border-style: none; }
+  #org-info-js_console-label
+    { font-size: 10px; font-weight: bold; white-space: nowrap; }
+  .org-info-js_search-highlight
+    { background-color: #ffff00; color: #000000; font-weight: bold; }
+  .org-svg { width: 90%; }
+  /*]]>*/-->
+</style>
+<script type="text/javascript">
+// @license magnet:?xt=urn:btih:e95b018ef3580986a04669f1b5879592219e2a7a&dn=public-domain.txt Public Domain
+<!--/*--><![CDATA[/*><!--*/
+     function CodeHighlightOn(elem, id)
+     {
+       var target = document.getElementById(id);
+       if(null != target) {
+         elem.classList.add("code-highlighted");
+         target.classList.add("code-highlighted");
+       }
+     }
+     function CodeHighlightOff(elem, id)
+     {
+       var target = document.getElementById(id);
+       if(null != target) {
+         elem.classList.remove("code-highlighted");
+         target.classList.remove("code-highlighted");
+       }
+     }
+    /*]]>*///-->
+// @license-end
+</script>
+</head>
+<body>
+<div id="content">
+<div id="table-of-contents">
+<h2>Table of Contents</h2>
+<div id="text-table-of-contents">
+<ul>
+<li><a href="#orgcb7a42f">Planning The HoTT Game</a>
+<ul>
+<li><a href="#org86f8abf">Aims of the HoTT Game</a></li>
+<li><a href="#org891bd67">Barriers</a></li>
+<li><a href="#org865979d">Format</a></li>
+<li><a href="#org7cb3a5d">Content</a></li>
+<li><a href="#org313668c">Debriefs</a></li>
+</ul>
+</li>
+</ul>
+</div>
+</div>
+
+<div id="outline-container-orgcb7a42f" class="outline-2">
+<h2 id="orgcb7a42f">Planning The HoTT Game</h2>
+<div class="outline-text-2" id="text-orgcb7a42f">
+</div>
+<div id="outline-container-org86f8abf" class="outline-3">
+<h3 id="org86f8abf">Aims of the HoTT Game</h3>
+<div class="outline-text-3" id="text-org86f8abf">
+<ul class="org-ul">
+<li>To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT</li>
+<li>[?] Work towards showing an interesting result in HoTT</li>
+<li>Try to balance hiding cubical implementations whilst exploiting their advantages</li>
+</ul>
+</div>
+</div>
+
+<div id="outline-container-org891bd67" class="outline-3">
+<h3 id="org891bd67">Barriers</h3>
+<div class="outline-text-3" id="text-org891bd67">
+<ul class="org-ul">
+<li>HOLD Installation of emacs</li>
+<li>TODO Usage of emacs</li>
+<li>TODO General type theoretic foundations</li>
+<li>TODO Cubical type theory</li>
+</ul>
+</div>
+</div>
+
+<div id="outline-container-org865979d" class="outline-3">
+<h3 id="org865979d">Format</h3>
+<div class="outline-text-3" id="text-org865979d">
+<ul class="org-ul">
+<li>[?] Everything done in .agda files</li>
+<li>Partially written code with spaces for participants to fill in + answer files</li>
+<li>Levels set out with mini-bosses like in Nat Num Game, but with an overall boss</li>
+<li>[?] Side quests</li>
+<li>References to Harper lectures and HoTT book</li>
+</ul>
+</div>
+</div>
+
+<div id="outline-container-org7cb3a5d" class="outline-3">
+<h3 id="org7cb3a5d">Content</h3>
+<div class="outline-text-3" id="text-org7cb3a5d">
+<ul class="org-ul">
+<li>emacs usage</li>
+<li>agda usage
+<ul class="org-ul">
+<li>basic commands (all covered in <a href="https://agda.readthedocs.io/en/v2.6.0.1/getting-started/quick-guide.html">https://agda.readthedocs.io/en/v2.6.0.1/getting-started/quick-guide.html</a>)</li>
+<li>recommend doom emacs</li>
+<li>implicit/explicit arguments</li>
+<li>holes and inferred types</li>
+<li><code>_+_</code> vs <code>plus__</code></li>
+</ul></li>
+<li>type theory basics
+<ul class="org-ul">
+<li>meta (judgemental/definitional) equality vs internal (propositional) equality
+<ul class="org-ul">
+<li>function extensionality</li>
+</ul></li>
+<li>type formation
+<ul class="org-ul">
+<li>inductive types
+<ul class="org-ul">
+<li>(side Q) positive and negative constructions of Pi/Sigma types</li>
+<li><code>data</code> and <code>record</code></li>
+</ul></li>
+</ul></li>
+<li>universes</li>
+<li>recursors / pattern matching</li>
+<li>(side Q) some natural number exercises as early evidence of being able to &rsquo;do maths&rsquo;?</li>
+<li>different notions of equivalence
+<ol class="org-ol">
+<li>fibers contractable</li>
+<li>quasi-inverse</li>
+<li>zig-zag</li>
+</ol></li>
+<li>(side Q) types are infinity groupoids</li>
+<li>extra paths (univalence, fun ext, HITs)</li>
+</ul></li>
+<li>HoTT
+<ul class="org-ul">
+<li>basics
+<ol class="org-ol">
+<li>meta interval, identity type vs path type
+<ul class="org-ul">
+<li>mention identity type for compatability with other sources, but just use path type</li>
+</ul></li>
+<li>path type on other types</li>
+<li>dependent path type PathP vs path over</li>
+<li>univalence</li>
+<li>the (non)-issue of J in (Cu)TT</li>
+<li>isContr, isProp, isSet</li>
+<li>drawing pictures</li>
+</ol></li>
+<li>Structures, using univalence to transport
+<ol class="org-ol">
+<li>transporting results between isomorphic structures</li>
+</ol></li>
+<li>HITs, examples
+<ol class="org-ol">
+<li>the constructed interval</li>
+<li>booleans and covers</li>
+<li>S<sup>n</sup></li>
+<li>S<sup>1</sup> with 2 cw structures equiv</li>
+</ol></li>
+<li>Homotopy n-types
+<ol class="org-ol">
+<li>homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT
+<ul class="org-ul">
+<li>in particular sigma types</li>
+</ul></li>
+</ol></li>
+</ul></li>
+</ul>
+</div>
+</div>
+
+<div id="outline-container-org313668c" class="outline-3">
+<h3 id="org313668c">Debriefs</h3>
+<div class="outline-text-3" id="text-org313668c">
+<ul class="org-ul">
+<li>2021 July 15; Homotopy n-types
+<ul class="org-ul">
+<li>watched (Harper) lecture 15 on Sets being closed under type formations -&gt;- motivates showing in Agda Sets closed under Sigma.</li>
+<li>Harper does product case, claiming sigma case follows analogously,</li>
+<li>attempt proof in Cubical Agda but highly non-obvious how to use that fibers are Sets.</li>
+<li>difficulty is that PathP not in one fiber, but PathOver is, AND PathOver &lt;-&gt; PathP NON-obvious</li>
+<li>Easy to generalize situation to n-types being closed under Sigma (7.1.8 in HoTT book), we showed this assuming PathPIsoPath</li>
+</ul></li>
+</ul>
+</div>
+</div>
+</div>
+</div>
+<div id="postamble" class="status">
+<p class="author">Author: JLH KL</p>
+<p class="date">Created: 2021-07-19 Mon 18:31</p>
+</div>
+</body>
+</html>
--- a/Plan.md
+++ b/Plan.md
@ -1,72 +1,119 @@
-# Planning The HoTT Game

-## Aims of the HoTT Game
- To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT
- [?] Work towards showing an interesting result in HoTT
- Try to balance hiding cubical implementations whilst exploiting their advantages
+# Table of Contents

-## Barriers
- HOLD Installation of emacs
- TODO Usage of emacs
- TODO General type theoretic foundations
- TODO Cubical type theory
+1.  [Aims of the HoTT Game](#org45da28b)
+    1.  [To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT](#org6c86aa4)
+    2.  [Work towards showing an interesting result in HoTT](#org5c370bf)
+    3.  [Try to balance hiding cubical implementations whilst exploiting their advantages](#org2cc236e)
+2.  [Barriers](#org483c28e)
+    1.  [Installation of emacs](#orgfaee064)
+    2.  [Usage of emacs](#org4ec8663)
+    3.  [General type theoretic foundations](#orgd6212c3)
+    4.  [Cubical type theory](#orgdb053bf)

-## Format
- [?] Everything done in .agda files
- Partially written code with spaces for participants to fill in + answer files
- Levels set out with mini-bosses like in Nat Num Game, but with an overall boss
- [?] Side quests
- References to Harper lectures and HoTT book

-# Content
-<!-- listing topics we have pursued, NO ordering -->
- emacs usage
- agda usage
-  - basic commands (all covered in https://agda.readthedocs.io/en/v2.6.0.1/getting-started/quick-guide.html)
-  - recommend doom emacs? -> basic doom usage and command differences with nude agda.
-  - implicit/explicit arguments
-  - holes and inferred types
-  - `_+_` and `plus__`
- type theory basics
-  - meta (judgemental/definitional) equality vs internal (propositional) equality
-    - function extensionality
-  - type formation
-  - universes
-  - recursors / pattern matching
-  - (side Q) some natural number exercises as early evidence of being able to 'do maths'?
-  - different notions of equivalence
-    a) fibers contractable
-    b) quasi-inverse
-    c) zig-zag
-  - (side Q) types are infinity groupoids
-  - inductive types
-    - (side Q) positive and negative constructions of Pi/Sigma types
-    - `data` and `record`
- HoTT
-  - basics
-    a) meta interval, identity type vs path type
-      - mention identity type for compatability with other sources, but just use path type
-    b) path type on other types
-    c) dependent path type PathP vs path over
-    d) univalence
-    e) the (non)-issue of J in (Cu)TT
-    f) isContr, isProp, isSet
-    g) drawing pictures
-  - Structures, univalence and transport
-    a) transporting results between isomorphic structures
-  - HITs, examples
-    a) the constructed interval
-    b) booleans and covers
-    c) S^n
-    d)
-  - Homotopy n-types
-    a) homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT
-       * in particular sigma types
+<a id="org45da28b"></a>
+
+# Aims of the HoTT Game
+
+
+<a id="org6c86aa4"></a>
+
+## To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT
+
+
+<a id="org5c370bf"></a>
+
+## [?] Work towards showing an interesting result in HoTT
+
+
+<a id="org2cc236e"></a>
+
+## Try to balance hiding cubical implementations whilst exploiting their advantages
+
+
+<a id="org483c28e"></a>
+
+# Barriers
+
+
+<a id="orgfaee064"></a>
+
+## HOLD Installation of emacs
+
+
+<a id="org4ec8663"></a>
+
+## TODO Usage of emacs
+
+
+<a id="orgd6212c3"></a>
+
+## TODO General type theoretic foundations
+
+
+<a id="orgdb053bf"></a>
+
+## TODO Cubical type theory
+
+\## Format
+
+-   [?] Everything done in .agda files
+-   Partially written code with spaces for participants to fill in + answer files
+-   Levels set out with mini-bosses like in Nat Num Game, but with an overall boss
+-   [?] Side quests
+-   References to Harper lectures and HoTT book
+
+<!&#x2013; listing topics we have pursued, NO ordering &#x2013;>
+
+-   emacs usage
+-   agda usage
+    -   basic commands (all covered in <https://agda.readthedocs.io/en/v2.6.0.1/getting-started/quick-guide.html>)
+    -   recommend doom emacs
+    -   implicit/explicit arguments
+    -   holes and inferred types
+    -   \`\_+\_\` and \`plus\_\_\`
+-   type theory basics
+    -   meta (judgemental/definitional) equality vs internal (propositional) equality
+        -   function extensionality
+    -   type formation
+        -   inductive types
+            -   (side Q) positive and negative constructions of Pi/Sigma types
+            -   \`data\` and \`record\`
+    -   universes
+    -   recursors / pattern matching
+    -   (side Q) some natural number exercises as early evidence of being able to &rsquo;do maths&rsquo;?
+    -   different notions of equivalence
+        1.  fibers contractable
+        2.  quasi-inverse
+        3.  zig-zag
+    -   (side Q) types are infinity groupoids
+    -   extra paths (univalence, fun ext, HITs)
+-   HoTT
+    -   basics
+        1.  meta interval, identity type vs path type
+            -   mention identity type for compatability with other sources, but just use path type
+        2.  path type on other types
+        3.  dependent path type PathP vs path over
+        4.  univalence
+        5.  the (non)-issue of J in (Cu)TT
+        6.  isContr, isProp, isSet
+        7.  drawing pictures
+    -   Structures, using univalence to transport
+        1.  transporting results between isomorphic structures
+    -   HITs, examples
+        1.  the constructed interval
+        2.  booleans and covers
+        3.  S<sup>n</sup>
+        4.  S<sup>1</sup> with 2 cw structures equiv
+    -   Homotopy n-types
+        1.  homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT
+            -   in particular sigma types
+
+-   2021 July 15; Homotopy n-types
+    -   watched (Harper) lecture 15 on Sets being closed under type formations ->- motivates showing in Agda Sets closed under Sigma.
+    -   Harper does product case, claiming sigma case follows analogously,
+    -   attempt proof in Cubical Agda but highly non-obvious how to use that fibers are Sets.
+    -   difficulty is that PathP not in one fiber, but PathOver is, AND PathOver <-> PathP NON-obvious
+    -   Easy to generalize situation to n-types being closed under Sigma (7.1.8 in HoTT book), we showed this assuming PathPIsoPath

-# Debriefs
- 2021 July 15; Homotopy n-types
-  - watched (Harper) lecture 15 on Sets being closed under type formations ->- motivates showing in Agda Sets closed under Sigma.
-  - Harper does product case, claiming sigma case follows analogously,
-  - attempt proof in Cubical Agda but highly non-obvious how to use that fibers are Sets.
-  - difficulty is that PathP not in one fiber, but PathOver is, AND PathOver <-> PathP NON-obvious
-  - Easy to generalize situation to n-types being closed under Sigma (7.1.8 in HoTT book), we showed this assuming PathPIsoPath
--- a/Plan.org
+++ b/Plan.org
@ -1,32 +1,36 @@
-# Planning The HoTT Game
+#+OPTIONS: num:nil
+#+AUTHOR: JLH
+#+AUTHOR: KL

-## Aims of the HoTT Game
- To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT
- [?] Work towards showing an interesting result in HoTT
- Try to balance hiding cubical implementations whilst exploiting their advantages
+* Planning The HoTT Game

-## Barriers
- HOLD Installation of emacs
- TODO Usage of emacs
- TODO General type theoretic foundations
- TODO Cubical type theory
+** Aims of the HoTT Game
+  - To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT
+  - [?] Work towards showing an interesting result in HoTT
+  - Try to balance hiding cubical implementations whilst exploiting their advantages

-## Format
- [?] Everything done in .agda files
- Partially written code with spaces for participants to fill in + answer files
- Levels set out with mini-bosses like in Nat Num Game, but with an overall boss
- [?] Side quests
- References to Harper lectures and HoTT book
+** Barriers
+  - HOLD Installation of emacs
+  - TODO Usage of emacs
+  - TODO General type theoretic foundations
+  - TODO Cubical type theory

-# Content
-<!-- listing topics we have pursued, NO ordering -->
+** Format
+  - [?] Everything done in .agda files
+  - Partially written code with spaces for participants to fill in + answer files
+  - Levels set out with mini-bosses like in Nat Num Game, but with an overall boss
+  - [?] Side quests
+  - References to Harper lectures and HoTT book
+
+** Content
+# listing topics we have pursued, NO ordering
 - emacs usage
 - agda usage
  - basic commands (all covered in https://agda.readthedocs.io/en/v2.6.0.1/getting-started/quick-guide.html)
-  - recommend doom emacs? -> basic doom usage and command differences with nude agda.
+  - recommend doom emacs
  - implicit/explicit arguments
  - holes and inferred types
-  - `_+_` and `plus__`
+  - src_elisp{(_+_)} and src_elisp{(plus__)}
 - type theory basics
  - meta (judgemental/definitional) equality vs internal (propositional) equality
    - function extensionality
@ -64,7 +68,7 @@
    a) homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT
       * in particular sigma types

-# Debriefs
+** Debriefs
 - 2021 July 15; Homotopy n-types
  - watched (Harper) lecture 15 on Sets being closed under type formations ->- motivates showing in Agda Sets closed under Sigma.
  - Harper does product case, claiming sigma case follows analogously,