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3 <html xmlns="http://www.w3.org/1999/xhtml" xmlns:ld="http://lambdadelta.info/" dir="ltr" lang="en-us"><head><meta http-equiv="Content-Language" content="en-us"/><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/><meta http-equiv="Content-Style-Type" content="text/css"/><meta name="author" content="Ferruccio Guidi"/><meta name="description" content="\lambda\delta home page"/><title>\lambda\delta home page</title><link rel="stylesheet" type="text/css" href="http://lambdadelta.info/css/ld_web.css"/><link rel="stylesheet" type="text/css" href="http://lambdadelta.info/css/lddl.css"/><link rel="stylesheet" type="text/css" href="http://lambdadelta.info/css/xhtbl.css"/><link rel="shortcut icon" href="http://lambdadelta.info/images/crux_16.ico"/></head><body lang="en-US"><div class="spacer"><a href="http://lambdadelta.info/"><img class="icon32" alt="[\lambda\delta home]" title="\lambda\delta home" src="http://lambdadelta.info/images/crux_32.png"/></a></div><div class="head1">cic:/matita/lambdadelta/ground_2/ (background for ฮปฮด version 2)</div><div class="spacer"><img class="rule" alt="[Spacer]" title="\lambda\delta rainbow rule" src="http://lambdadelta.info/images/rainbow.png"/></div><div class="spacer"><br/></div><div class="text"><table cellpadding="4" cellspacing="0"><tbody><tr><td class="snns capitalize italic sky"><a href="http://lambdadelta.info/home.html">home</a></td><td class="snns capitalize italic magenta"><a href="http://lambdadelta.info/news.html">news</a></td><td class="snns capitalize italic white"><a href="http://lambdadelta.info/specification.html">specification</a></td><td class="snnn capitalize italic white"><br/></td><td class="snnn capitalize italic white"><br/></td><td class="snns capitalize italic orange"><a href="http://lambdadelta.info/documentation.html">documentation</a></td><td class="snns capitalize italic green"><a href="http://lambdadelta.info/implementation.html">implementation</a></td><td class="ssnn capitalize italic green"><br/></td></tr><tr><td class="snns capitalize sky"><a href="http://lambdadelta.info/home.html#foreword">foreword</a></td><td class="snns capitalize magenta"><a href="http://lambdadelta.info/news.html#milestones">milestones</a></td><td class="snns capitalize white"><a href="http://lambdadelta.info/specification.html#v2">version 2</a></td><td class="snnn capitalize white">(<a href="http://lambdadelta.info/ground_2.html">background</a> - <a href="http://lambdadelta.info/basic_2.html">core</a> - <a href="http://lambdadelta.info/apps_2.html">applications</a>)</td><td class="snnn capitalize white"><br/></td><td class="snns capitalize orange"><a href="http://lambdadelta.info/documentation.html#v2">version 2</a></td><td class="snns capitalize green"><a href="http://lambdadelta.info/implementation.html#helena">helena</a></td><td class="ssnn capitalize green"><a href="http://lambdadelta.info/osn/">Open Symbolic Notation (OSN)</a></td></tr><tr><td class="snss capitalize sky"><a href="http://lambdadelta.info/home.html#citations">citations</a></td><td class="snss capitalize magenta"><a href="http://lambdadelta.info/news.html#visibility">visibility</a></td><td class="snss capitalize white"><a href="http://lambdadelta.info/specification.html#v1">version 1</a></td><td class="snsn capitalize white">(<a href="http://lambdadelta.info/ground_1.html">background</a> - <a href="http://lambdadelta.info/basic_1.html">core</a>)</td><td class="snsn capitalize white">(<a href="http://lambdadelta.info/static/matita/lambdadelta/">static HELM directory</a>)</td><td class="snss capitalize orange"><a href="http://lambdadelta.info/documentation.html#v1">version 1</a></td><td class="snss capitalize green"><a href="http://lambdadelta.info/implementation.html#lddl">library</a></td><td class="sssn capitalize green">(<a href="http://lambdadelta.info/static/lddl/">static LDDL directory</a>)</td></tr></tbody></table></div><div class="head2dx" id="summary">Summary of the Specification <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b4.png"/></div><div class="text">Here is a numerical account of the specification's contents
5 </div><div class="text"><table cellpadding="4" cellspacing="0"><tbody><tr><td class="snns capitalize italic gray">category</td><td class="snns italic gray">objects</td><td class="snnn right italic gray"><br/></td><td class="snnn italic gray"><br/></td><td class="snnn right italic gray"><br/></td><td class="snnn italic gray"><br/></td><td class="ssnn right italic gray"><br/></td></tr><tr><td class="snns capitalize italic cyan">sizes</td><td class="snns italic cyan">files</td><td class="snnn right italic cyan">93</td><td class="snns italic cyan">characters</td><td class="snnn right italic cyan">135543</td><td class="snns italic cyan">nodes</td><td class="ssnn right italic cyan">314125</td></tr><tr><td class="snns capitalize italic green">propositions</td><td class="snns italic green">theorems</td><td class="snnn right italic green">38</td><td class="snns italic green">lemmas</td><td class="snnn right italic green">647</td><td class="snns italic green">total</td><td class="ssnn right italic green">685</td></tr><tr><td class="snss capitalize italic yellow">concepts</td><td class="snss italic yellow">declared</td><td class="snsn right italic yellow">63</td><td class="snss italic yellow">defined</td><td class="snsn right italic yellow">67</td><td class="snss italic yellow">total</td><td class="sssn right italic yellow">130</td></tr></tbody></table></div><ul><li><span class="emph alpha">2016 April 18.</span>
6 Generic rt-transition counter (rtc).
7 </li></ul><ul><li><span class="emph alpha">2016 March 4.</span>
8 Platform-independent multiple relocation (rtmap).
9 </li></ul><ul><li><span class="emph alpha">2016 January 20.</span>
10 Multiple relocation with streams of naturals.
11 </li></ul><ul><li><span class="emph alpha">2015 October 11.</span>
12 Multiple relocation with lists of booleans.
13 </li></ul><ul><li><span class="emph alpha">2013 November 27.</span>
14 Natural numbers with infinity (ynat).
15 </li></ul><ul><li><span class="emph alpha">2011 August 10.</span>
17 </li></ul><div class="head2dx" id="structure">Logical Structure of the Specification <img class="icon37" alt="[butterfly]" title="\lambda\delta butterfly" src="http://lambdadelta.info/images/b4.png"/></div><div class="text">This table reports the specification's components and their planes.
18 </div><div class="text"><table cellpadding="4" cellspacing="0"><tbody><tr><td class="snns top capitalize italic gray">component</td><td class="snns top italic gray">plane</td><td class="snns top gray">files</td><td class="snnn top gray"><br/></td><td class="snnn top gray"><br/></td><td class="snnn top gray"><br/></td><td class="snnn top gray"><br/></td><td class="snnn top gray"><br/></td><td class="snnn top gray"><br/></td><td class="snnn top gray"><br/></td><td class="snnn top gray"><br/></td><td class="snnn top gray"><br/></td><td class="snnn top gray"><br/></td><td class="snnn top gray"><br/></td><td class="snnn top gray"><br/></td><td class="snnn top gray"><br/></td><td class="snnn top gray"><br/></td><td class="snnn top gray"><br/></td><td class="snnn top gray"><br/></td><td class="ssnn top gray"><br/></td></tr><tr><td class="snns top capitalize italic water">generic rt-transition counter</td><td class="snns top italic water"/><td class="snns top water">rtc ( โฉ?,?,?,?โช ) ( ๐๐ ) ( ๐๐ ) ( ๐๐ )</td><td class="snnn top water">rtc_isrc ( ๐๐โฆ?, ?โฆ )</td><td class="snnn top water">rtc_shift ( โ? )</td><td class="snnn top water">rtc_max ( ? โจ ? )</td><td class="snnn top water">rtc_plus ( ? + ? )</td><td class="snnn top water"><br/></td><td class="snnn top water"><br/></td><td class="snnn top water"><br/></td><td class="snnn top water"><br/></td><td class="snnn top water"><br/></td><td class="snnn top water"><br/></td><td class="snnn top water"><br/></td><td class="snnn top water"><br/></td><td class="snnn top water"><br/></td><td class="snnn top water"><br/></td><td class="snnn top water"><br/></td><td class="snnn top water"><br/></td><td class="ssnn top water"><br/></td></tr><tr><td class="snns top capitalize italic green">multiple relocation</td><td class="snns top italic green"/><td class="snns top green">rtmap</td><td class="snnn top green">rtmap_eq ( ? โ ? )</td><td class="snnn top green">rtmap_pushs ( โ*[?]? )</td><td class="snnn top green">rtmap_tl ( โซฑ? )</td><td class="snnn top green">rtmap_tls ( โซฑ*[?]? )</td><td class="snnn top green">rtmap_isid ( ๐โฆ?โฆ )</td><td class="snnn top green">rtmap_id</td><td class="snnn top green">rtmap_fcla ( ๐โฆ?โฆ โก ? )</td><td class="snnn top green">rtmap_isfin ( ๐
โฆ?โฆ )</td><td class="snnn top green">rtmap_isuni ( ๐โฆ?โฆ )</td><td class="snnn top green">rtmap_uni ( ๐โด?โต )</td><td class="snnn top green">rtmap_sle ( ? โ ? )</td><td class="snnn top green">rtmap_sand ( ? โ ? โก ? )</td><td class="snnn top green">rtmap_sor ( ? โ ? โก ? )</td><td class="snnn top green">rtmap_at ( @โฆ?,?โฆ โก ? )</td><td class="snnn top green">rtmap_istot ( ๐โฆ?โฆ )</td><td class="snnn top green">rtmap_after ( ? โ ? โก ? )</td><td class="ssnn top green">rtmap_coafter ( ? ~โ ? โก ? )</td></tr><tr><td class="nnns top capitalize italic green"><br/></td><td class="nnns top italic green"><br/></td><td class="snns top green">nstream ( โ? ) ( โซฏ? )</td><td class="snnn top green">nstream_eq</td><td class="snnn top green"/><td class="snnn top green"/><td class="snnn top green"/><td class="snnn top green">nstream_isid</td><td class="snnn top green">nstream_id ( ๐๐ )</td><td class="snnn top green"/><td class="snnn top green"/><td class="snnn top green"/><td class="snnn top green"/><td class="snnn top green"/><td class="snnn top green">nstream_sand</td><td class="snnn top green"/><td class="snnn top green"/><td class="snnn top green">nstream_istot ( ?@โด?โต )</td><td class="snnn top green">nstream_after ( ? โ ? )</td><td class="ssnn top green">nstream_coafter ( ? ~โ ? )</td></tr><tr><td class="nnns top capitalize italic green"><br/></td><td class="nnns top italic green"><br/></td><td class="snns top green">mr2</td><td class="snnn top green">mr2_at ( @โฆ?,?โฆ โก ? )</td><td class="snnn top green">mr2_plus ( ? + ? )</td><td class="snnn top green">mr2_minus ( ? โญ ? โก ? )</td><td class="snnn top green"><br/></td><td class="snnn top green"><br/></td><td class="snnn top green"><br/></td><td class="snnn top green"><br/></td><td class="snnn top green"><br/></td><td class="snnn top green"><br/></td><td class="snnn top green"><br/></td><td class="snnn top green"><br/></td><td class="snnn top green"><br/></td><td class="snnn top green"><br/></td><td class="snnn top green"><br/></td><td class="snnn top green"><br/></td><td class="snnn top green"><br/></td><td class="ssnn top green"><br/></td></tr><tr><td class="snns top capitalize italic grass">natural numbers with infinity</td><td class="snns top italic grass"/><td class="snns top grass">ynat ( โ )</td><td class="snnn top grass">ynat_pred ( โซฐ? )</td><td class="snnn top grass">ynat_succ ( โซฏ? )</td><td class="snnn top grass">ynat_le ( ? โค ? )</td><td class="snnn top grass">ynat_lt ( ? < ? )</td><td class="snnn top grass">ynat_plus ( ? + ? )</td><td class="snnn top grass"><br/></td><td class="snnn top grass"><br/></td><td class="snnn top grass"><br/></td><td class="snnn top grass"><br/></td><td class="snnn top grass"><br/></td><td class="snnn top grass"><br/></td><td class="snnn top grass"><br/></td><td class="snnn top grass"><br/></td><td class="snnn top grass"><br/></td><td class="snnn top grass"><br/></td><td class="snnn top grass"><br/></td><td class="ssnn top grass"><br/></td></tr><tr><td class="snns top capitalize italic yellow">extensions to the library</td><td class="snns top italic yellow"/><td class="snns top yellow">stream ( ? @ ? )</td><td class="snnn top yellow">stream_eq ( ? โ ? )</td><td class="snnn top yellow">stream_hdtl ( โ? )</td><td class="snnn top yellow">stream_tls ( โ*[?]? )</td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="ssnn top yellow"><br/></td></tr><tr><td class="nnns top capitalize italic yellow"><br/></td><td class="nnns top italic yellow"><br/></td><td class="snns top yellow">list ( โ ) ( ? @ ? ) ( |?| )</td><td class="snnn top yellow">list2 ( โ ) ( {?,?} @ ? ) ( ? @@ ? ) ( |?| )</td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="ssnn top yellow"><br/></td></tr><tr><td class="nnns top capitalize italic yellow"><br/></td><td class="nnns top italic yellow"><br/></td><td class="snns top yellow">bool ( โป ) ( โ )</td><td class="snnn top yellow">arith ( ?^? ) ( โซฏ? ) ( โซฐ? ) ( ? โจ ? ) ( ? โง ? )</td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="ssnn top yellow"><br/></td></tr><tr><td class="nnns top capitalize italic yellow"><br/></td><td class="nnns top italic yellow"><br/></td><td class="snns top yellow">star</td><td class="snnn top yellow">lstar</td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="snnn top yellow"><br/></td><td class="ssnn top yellow"><br/></td></tr><tr><td class="snns top capitalize italic orange">generated logical decomposables</td><td class="snns top italic orange"/><td class="snns top orange">xoa ( โโ ) ( โจโจ ) ( โงโง )</td><td class="snnn top orange">xoa_props ( โฅ ) ( โค )</td><td class="snnn top orange"><br/></td><td class="snnn top orange"><br/></td><td class="snnn top orange"><br/></td><td class="snnn top orange"><br/></td><td class="snnn top orange"><br/></td><td class="snnn top orange"><br/></td><td class="snnn top orange"><br/></td><td class="snnn top orange"><br/></td><td class="snnn top orange"><br/></td><td class="snnn top orange"><br/></td><td class="snnn top orange"><br/></td><td class="snnn top orange"><br/></td><td class="snnn top orange"><br/></td><td class="snnn top orange"><br/></td><td class="snnn top orange"><br/></td><td class="ssnn top orange"><br/></td></tr><tr><td class="snss top capitalize italic red"/><td class="snss top italic red"/><td class="snss top red"><br/></td><td class="snsn top red"><br/></td><td class="snsn top red"><br/></td><td class="snsn top red"><br/></td><td class="snsn top red"><br/></td><td class="snsn top red"><br/></td><td class="snsn top red"><br/></td><td class="snsn top red"><br/></td><td class="snsn top red"><br/></td><td class="snsn top red"><br/></td><td class="snsn top red"><br/></td><td class="snsn top red"><br/></td><td class="snsn top red"><br/></td><td class="snsn top red"><br/></td><td class="snsn top red"><br/></td><td class="snsn top red"><br/></td><td class="snsn top red"><br/></td><td class="sssn top red"><br/></td></tr></tbody></table></div><div 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