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<!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">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1" />
<link href="coqdoc.css" rel="stylesheet" type="text/css" />
<title>Combi.Combi.stdtab: Standard Tableaux</title>
</head>
<body>
<div id="page">
<div id="header">
</div>
<div id="main">
<h1 class="libtitle">Library Combi.Combi.stdtab: Standard Tableaux</h1>
<div class="code">
</div>
<div class="doc">
</div>
<div class="code">
</div>
<div class="doc">
<a id="lab84"></a><h1 class="section">Standard Tableaux</h1>
<div class="paragraph"> </div>
We define the following notions:
<div class="paragraph"> </div>
<ul class="doclist">
<li> <span class="inlinecode"><span class="id" title="var">append_nth</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> <span class="inlinecode"><span class="id" title="var">b</span></span> <span class="inlinecode"><span class="id" title="var">i</span></span> == <span class="inlinecode"><span class="id" title="var">t</span></span> with <span class="inlinecode"><span class="id" title="var">b</span></span> appended to its <span class="inlinecode"><span class="id" title="var">i</span></span>-th row
<div class="paragraph"> </div>
</li>
<li> <span class="inlinecode"><span class="id" title="var">is_stdtab</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> == <span class="inlinecode"><span class="id" title="var">t</span></span> is a *standard tableau* that is a tableau whose
row reading is a standard word
</li>
<li> <span class="inlinecode"><span class="id" title="var">last_big</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> <span class="inlinecode"><span class="id" title="var">b</span></span> == the index of the first row of <span class="inlinecode"><span class="id" title="var">t</span></span> which ends with <span class="inlinecode"><span class="id" title="var">b</span></span>
</li>
<li> <span class="inlinecode"><span class="id" title="var">remn</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> == remove the largest entry ie <span class="inlinecode"><span class="id" title="var">n</span></span> from a standard tableau of size <span class="inlinecode"><span class="id" title="var">n</span></span>
</li>
<li> <span class="inlinecode"><span class="id" title="var">conj_tab</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> == the conjugate standard tableau of <span class="inlinecode"><span class="id" title="var">t</span></span> (this is indeed a tableau
when <span class="inlinecode"><span class="id" title="var">t</span></span> is itself a standard tableau.
</li>
</ul>
<div class="paragraph"> </div>
Bijection between Yamanouchi words and standard tableau
<div class="paragraph"> </div>
<ul class="doclist">
<li> <span class="inlinecode"><span class="id" title="var">stdtab_of_yam</span></span> <span class="inlinecode"><span class="id" title="var">y</span></span> == the standard tableau associated to <span class="inlinecode"><span class="id" title="var">y</span></span>
</li>
<li> <span class="inlinecode"><span class="id" title="var">yam_of_stdtab</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> == the Yamanouchi words associated to <span class="inlinecode"><span class="id" title="var">t</span></span>
</li>
</ul>
<div class="paragraph"> </div>
Sigma type for standard tableaux:
<div class="paragraph"> </div>
<ul class="doclist">
<li> <span class="inlinecode"><span class="id" title="var">is_stdtab_of_shape</span></span> <span class="inlinecode"><span class="id" title="var">sh</span></span> == a predicate for standard tableau of shape <span class="inlinecode"><span class="id" title="var">sh</span></span>.
</li>
<li> <span class="inlinecode"><span class="id" title="var">stdtabsh</span></span> <span class="inlinecode"><span class="id" title="var">sh</span></span> == a sigma type for <span class="inlinecode"><span class="id" title="var">is_stdtab_of_shape</span></span> <span class="inlinecode"><span class="id" title="var">sh</span></span> where <span class="inlinecode"><span class="id" title="var">sh</span></span> is an
integer partition (of type <span class="inlinecode"><span class="id" title="var">intpart</span></span>). This is canonically a
<span class="inlinecode"><span class="id" title="var">finType</span></span>.
<div class="paragraph"> </div>
</li>
<li> <span class="inlinecode"><span class="id" title="var">is_stdtab_of_n</span></span> <span class="inlinecode"><span class="id" title="var">n</span></span> == a predicate for standard tableau of size <span class="inlinecode"><span class="id" title="var">n</span></span>
</li>
<li> <span class="inlinecode"><span class="id" title="var">stdtabn</span></span> <span class="inlinecode"><span class="id" title="var">n</span></span> == a sigma type for <span class="inlinecode"><span class="id" title="var">is_stdtab_of_n</span></span> <span class="inlinecode"><span class="id" title="var">n</span></span>. This is canonically a
<span class="inlinecode"><span class="id" title="var">finType</span></span>.
<div class="paragraph"> </div>
</li>
<li> <span class="inlinecode"><span class="id" title="var">shape_deg</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> == if t is of type <span class="inlinecode"><span class="id" title="var">stdtabn</span></span> <span class="inlinecode"><span class="id" title="var">n</span></span>, the shape of <span class="inlinecode"><span class="id" title="var">t</span></span> in the
sigma type <span class="inlinecode">'<span class="id" title="var">P_n</span></span>
<div class="paragraph"> </div>
</li>
<li> <span class="inlinecode"><span class="id" title="var">hyper_stdtabsh</span></span> <span class="inlinecode"><span class="id" title="var">sh</span></span> == the hyperstandard tableau of shape <span class="inlinecode"><span class="id" title="var">sh</span></span> <span class="inlinecode">:</span> <span class="inlinecode"><span class="id" title="var">intpart</span></span>,
that is the tableau obtained by filling the rows with consecutive
numbers, from bottom to top (in French conventions)
<div class="paragraph"> </div>
</li>
<li> <span class="inlinecode"><span class="id" title="var">conj_stdtabn</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> == the conjugate of <span class="inlinecode"><span class="id" title="var">t</span></span> <span class="inlinecode">:</span> <span class="inlinecode"><span class="id" title="var">stdtabn</span></span> <span class="inlinecode"><span class="id" title="var">n</span></span> in type <span class="inlinecode"><span class="id" title="var">stdtabn</span></span> <span class="inlinecode"><span class="id" title="var">n</span></span>
</li>
<li> <span class="inlinecode"><span class="id" title="var">conj_stdtabsh</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> == the conjugate of <span class="inlinecode"><span class="id" title="var">t</span></span> <span class="inlinecode">:</span> <span class="inlinecode"><span class="id" title="var">stdtabsh</span></span> <span class="inlinecode"><span class="id" title="var">sh</span></span>
in type <span class="inlinecode"><span class="id" title="var">stdtabsh</span></span> <span class="inlinecode">(<span class="id" title="var">conj_intpart</span></span> <span class="inlinecode"><span class="id" title="var">sh</span>)</span>
</li>
</ul>
<div class="paragraph"> </div>
<div class="paragraph"> </div>
Among the main results are the fact that <span class="inlinecode"><span class="id" title="var">stdtab_of_yam</span></span> and <span class="inlinecode"><span class="id" title="var">yam_of_stdtab</span></span>
are two converse bijections. That is:
<div class="paragraph"> </div>
<ul class="doclist">
<li> <span class="inlinecode"><span class="id" title="keyword">Lemma</span></span> <span class="inlinecode"><span class="id" title="var">stdtab_of_yamP</span></span> <span class="inlinecode"><span class="id" title="var">y</span></span> <span class="inlinecode">:</span> <span class="inlinecode"><span class="id" title="var">is_yam</span></span> <span class="inlinecode"><span class="id" title="var">y</span></span> <span class="inlinecode">-></span> <span class="inlinecode"><span class="id" title="var">is_stdtab</span></span> <span class="inlinecode">(<span class="id" title="var">stdtab_of_yam</span></span> <span class="inlinecode"><span class="id" title="var">y</span>).</span>
<div class="paragraph"> </div>
</li>
<li> <span class="inlinecode"><span class="id" title="keyword">Theorem</span></span> <span class="inlinecode"><span class="id" title="var">stdtab_of_yamK</span></span> <span class="inlinecode"><span class="id" title="var">y</span></span> <span class="inlinecode">:</span> <span class="inlinecode"><span class="id" title="var">is_yam</span></span> <span class="inlinecode"><span class="id" title="var">y</span></span> <span class="inlinecode">-></span> <span class="inlinecode"><span class="id" title="var">yam_of_stdtab</span></span> <span class="inlinecode">(<span class="id" title="var">stdtab_of_yam</span></span> <span class="inlinecode"><span class="id" title="var">y</span>)</span> <span class="inlinecode">=</span> <span class="inlinecode"><span class="id" title="var">y</span>.</span>
<div class="paragraph"> </div>
</li>
<li> <span class="inlinecode"><span class="id" title="keyword">Lemma</span></span> <span class="inlinecode"><span class="id" title="var">yam_of_stdtabP</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> <span class="inlinecode">:</span> <span class="inlinecode"><span class="id" title="var">is_stdtab</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> <span class="inlinecode">-></span> <span class="inlinecode"><span class="id" title="var">is_yam</span></span> <span class="inlinecode">(<span class="id" title="var">yam_of_stdtab</span></span> <span class="inlinecode"><span class="id" title="var">t</span>).</span>
<div class="paragraph"> </div>
</li>
<li> <span class="inlinecode"><span class="id" title="keyword">Theorem</span></span> <span class="inlinecode"><span class="id" title="var">yam_of_stdtabK</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> <span class="inlinecode">:</span> <span class="inlinecode"><span class="id" title="var">is_stdtab</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> <span class="inlinecode">-></span> <span class="inlinecode"><span class="id" title="var">stdtab_of_yam</span></span> <span class="inlinecode">(<span class="id" title="var">yam_of_stdtab</span></span> <span class="inlinecode"><span class="id" title="var">t</span>)</span> <span class="inlinecode">=</span>
<span class="inlinecode"><span class="id" title="var">t</span>.</span>
</li>
</ul>
<div class="paragraph"> </div>
Moreover, these bijections preserve the shape and therefore the size:
<div class="paragraph"> </div>
<ul class="doclist">
<li> <span class="inlinecode"><span class="id" title="keyword">Lemma</span></span> <span class="inlinecode"><span class="id" title="var">shape_stdtab_of_yam</span></span> <span class="inlinecode"><span class="id" title="var">y</span></span> <span class="inlinecode">:</span> <span class="inlinecode"><span class="id" title="var">shape</span></span> <span class="inlinecode">(<span class="id" title="var">stdtab_of_yam</span></span> <span class="inlinecode"><span class="id" title="var">y</span>)</span> <span class="inlinecode">=</span> <span class="inlinecode"><span class="id" title="var">evalseq</span></span> <span class="inlinecode"><span class="id" title="var">y</span>.</span>
<div class="paragraph"> </div>
</li>
<li> <span class="inlinecode"><span class="id" title="keyword">Lemma</span></span> <span class="inlinecode"><span class="id" title="var">shape_yam_of_stdtab</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> <span class="inlinecode">:</span> <span class="inlinecode"><span class="id" title="var">is_stdtab</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> <span class="inlinecode">-></span> <span class="inlinecode"><span class="id" title="var">evalseq</span></span> <span class="inlinecode">(<span class="id" title="var">yam_of_stdtab</span></span> <span class="inlinecode"><span class="id" title="var">t</span>)</span> <span class="inlinecode">=</span>
<span class="inlinecode"><span class="id" title="var">shape</span></span> <span class="inlinecode"><span class="id" title="var">t</span>.</span>
<div class="paragraph"> </div>
</li>
<li> <span class="inlinecode"><span class="id" title="keyword">Lemma</span></span> <span class="inlinecode"><span class="id" title="var">size_stdtab_of_yam</span></span> <span class="inlinecode"><span class="id" title="var">y</span></span> <span class="inlinecode">:</span> <span class="inlinecode"><span class="id" title="var">size_tab</span></span> <span class="inlinecode">(<span class="id" title="var">stdtab_of_yam</span></span> <span class="inlinecode"><span class="id" title="var">y</span>)</span> <span class="inlinecode">=</span> <span class="inlinecode"><span class="id" title="var">size</span></span> <span class="inlinecode"><span class="id" title="var">y</span>.</span>
<div class="paragraph"> </div>
</li>
<li> <span class="inlinecode"><span class="id" title="keyword">Lemma</span></span> <span class="inlinecode"><span class="id" title="var">size_yam_of_stdtab</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> <span class="inlinecode">:</span> <span class="inlinecode"><span class="id" title="var">is_stdtab</span></span> <span class="inlinecode"><span class="id" title="var">t</span></span> <span class="inlinecode">-></span> <span class="inlinecode"><span class="id" title="var">size</span></span> <span class="inlinecode">(<span class="id" title="var">yam_of_stdtab</span></span> <span class="inlinecode"><span class="id" title="var">t</span>)</span> <span class="inlinecode">=</span> <span class="inlinecode"><span class="id" title="var">size_tab</span></span>
<span class="inlinecode"><span class="id" title="var">t</span>.</span>
<div class="paragraph"> </div>
</li>
</ul>
</div>
<div class="code">
<span class="id" title="keyword">From</span> <span class="id" title="var">HB</span> <span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <span class="id" title="library">structures</span>.<br/>
<span class="id" title="keyword">From</span> <span class="id" title="var">mathcomp</span> <span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <span class="id" title="library">all_boot</span> <span class="id" title="library">order</span>.<br/>
<span class="id" title="keyword">From</span> <span class="id" title="var">mathcomp</span> <span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <span class="id" title="library">perm</span> <span class="id" title="library">fingroup</span>.<br/>
<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="Combi.SSRcomplements.tools.html#"><span class="id" title="library">tools</span></a> <a class="idref" href="Combi.Basic.combclass.html#"><span class="id" title="library">combclass</span></a> <a class="idref" href="Combi.Combi.partition.html#"><span class="id" title="library">partition</span></a> <a class="idref" href="Combi.Combi.Yamanouchi.html#"><span class="id" title="library">Yamanouchi</span></a> <a class="idref" href="Combi.Basic.ordtype.html#"><span class="id" title="library">ordtype</span></a> <a class="idref" href="Combi.Combi.std.html#"><span class="id" title="library">std</span></a> <a class="idref" href="Combi.Combi.tableau.html#"><span class="id" title="library">tableau</span></a>.<br/>
<br/>
<span class="id" title="keyword">Set Implicit Arguments</span>.<br/>
<br/>
<span class="id" title="keyword">Import</span> <span class="id" title="module">Order.Theory</span>.<br/>
<br/>
</div>
<div class="doc">
<a id="lab85"></a><h2 class="section">Appending on the n-th row</h2>
</div>
<div class="code">
<span class="id" title="keyword">Section</span> <a id="AppendNth" class="idref" href="#AppendNth"><span class="id" title="section">AppendNth</span></a>.<br/>
<br/>
<span class="id" title="keyword">Context</span> <a id="AppendNth.disp" class="idref" href="#AppendNth.disp"><span class="id" title="variable">disp</span></a> (<a id="AppendNth.T" class="idref" href="#AppendNth.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="Combi.Basic.ordtype.html#InhOrder.Exports.inhOrderType"><span class="id" title="abbreviation">inhOrderType</span></a> <a class="idref" href="Combi.Combi.stdtab.html#disp:1"><span class="id" title="variable">disp</span></a>).<br/>
<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">b</span> : <a class="idref" href="Combi.Combi.stdtab.html#AppendNth.T"><span class="id" title="variable">T</span></a>.<br/>
<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">t</span> : <span class="id" title="abbreviation">seq</span> (<span class="id" title="abbreviation">seq</span> <a class="idref" href="Combi.Combi.stdtab.html#AppendNth.T"><span class="id" title="variable">T</span></a>).<br/>
<br/>
<span class="id" title="keyword">Definition</span> <a id="append_nth" class="idref" href="#append_nth"><span class="id" title="definition">append_nth</span></a> <a id="t:3" class="idref" href="#t:3"><span class="id" title="binder">t</span></a> <a id="b:4" class="idref" href="#b:4"><span class="id" title="binder">b</span></a> <a id="i:5" class="idref" href="#i:5"><span class="id" title="binder">i</span></a> := <span class="id" title="definition">set_nth</span> <span class="id" title="notation">[::]</span> <a class="idref" href="Combi.Combi.stdtab.html#t:3"><span class="id" title="variable">t</span></a> <a class="idref" href="Combi.Combi.stdtab.html#i:5"><span class="id" title="variable">i</span></a> (<span class="id" title="definition">rcons</span> (<span class="id" title="definition">nth</span> <span class="id" title="notation">[::]</span> <a class="idref" href="Combi.Combi.stdtab.html#t:3"><span class="id" title="variable">t</span></a> <a class="idref" href="Combi.Combi.stdtab.html#i:5"><span class="id" title="variable">i</span></a>) <a class="idref" href="Combi.Combi.stdtab.html#b:4"><span class="id" title="variable">b</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="perm_append_nth" class="idref" href="#perm_append_nth"><span class="id" title="lemma">perm_append_nth</span></a> <a id="t:6" class="idref" href="#t:6"><span class="id" title="binder">t</span></a> <a id="x:7" class="idref" href="#x:7"><span class="id" title="binder">x</span></a> <a id="pos:8" class="idref" href="#pos:8"><span class="id" title="binder">pos</span></a> :<br/>
<span class="id" title="definition">perm_eq</span> (<a class="idref" href="Combi.Combi.tableau.html#to_word"><span class="id" title="definition">to_word</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#append_nth"><span class="id" title="definition">append_nth</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:6"><span class="id" title="variable">t</span></a> <a class="idref" href="Combi.Combi.stdtab.html#x:7"><span class="id" title="variable">x</span></a> <a class="idref" href="Combi.Combi.stdtab.html#pos:8"><span class="id" title="variable">pos</span></a>)) (<a class="idref" href="Combi.Combi.stdtab.html#x:7"><span class="id" title="variable">x</span></a> <span class="id" title="notation">::</span> <a class="idref" href="Combi.Combi.tableau.html#to_word"><span class="id" title="definition">to_word</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:6"><span class="id" title="variable">t</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="shape_append_nth" class="idref" href="#shape_append_nth"><span class="id" title="lemma">shape_append_nth</span></a> <a id="t:9" class="idref" href="#t:9"><span class="id" title="binder">t</span></a> <a id="b:10" class="idref" href="#b:10"><span class="id" title="binder">b</span></a> <a id="i:11" class="idref" href="#i:11"><span class="id" title="binder">i</span></a> : <span class="id" title="definition">shape</span> (<a class="idref" href="Combi.Combi.stdtab.html#append_nth"><span class="id" title="definition">append_nth</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:9"><span class="id" title="variable">t</span></a> <a class="idref" href="Combi.Combi.stdtab.html#b:10"><span class="id" title="variable">b</span></a> <a class="idref" href="Combi.Combi.stdtab.html#i:11"><span class="id" title="variable">i</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <span class="id" title="definition">incr_nth</span> (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:9"><span class="id" title="variable">t</span></a>) <a class="idref" href="Combi.Combi.stdtab.html#i:11"><span class="id" title="variable">i</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="size_append_nth" class="idref" href="#size_append_nth"><span class="id" title="lemma">size_append_nth</span></a> <a id="t:14" class="idref" href="#t:14"><span class="id" title="binder">t</span></a> <a id="b:15" class="idref" href="#b:15"><span class="id" title="binder">b</span></a> <a id="i:16" class="idref" href="#i:16"><span class="id" title="binder">i</span></a> : <a class="idref" href="Combi.Combi.tableau.html#size_tab"><span class="id" title="definition">size_tab</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#append_nth"><span class="id" title="definition">append_nth</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:14"><span class="id" title="variable">t</span></a> <a class="idref" href="Combi.Combi.stdtab.html#b:15"><span class="id" title="variable">b</span></a> <a class="idref" href="Combi.Combi.stdtab.html#i:16"><span class="id" title="variable">i</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <span class="id" title="notation">(</span><a class="idref" href="Combi.Combi.tableau.html#size_tab"><span class="id" title="definition">size_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:14"><span class="id" title="variable">t</span></a><span class="id" title="notation">).+1</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="get_tab_append_nth" class="idref" href="#get_tab_append_nth"><span class="id" title="lemma">get_tab_append_nth</span></a> (<a id="t:17" class="idref" href="#t:17"><span class="id" title="binder">t</span></a> : <span class="id" title="abbreviation">seq</span> (<span class="id" title="abbreviation">seq</span> <a class="idref" href="Combi.Combi.stdtab.html#AppendNth.T"><span class="id" title="variable">T</span></a>)) <a id="l:18" class="idref" href="#l:18"><span class="id" title="binder">l</span></a> <a id="i:19" class="idref" href="#i:19"><span class="id" title="binder">i</span></a> <a id="r:20" class="idref" href="#r:20"><span class="id" title="binder">r</span></a> <a id="c:21" class="idref" href="#c:21"><span class="id" title="binder">c</span></a> :<br/>
<a class="idref" href="Combi.Combi.tableau.html#get_tab"><span class="id" title="definition">get_tab</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#append_nth"><span class="id" title="definition">append_nth</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:17"><span class="id" title="variable">t</span></a> <a class="idref" href="Combi.Combi.stdtab.html#l:18"><span class="id" title="variable">l</span></a> <a class="idref" href="Combi.Combi.stdtab.html#i:19"><span class="id" title="variable">i</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="Combi.Combi.stdtab.html#r:20"><span class="id" title="variable">r</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="Combi.Combi.stdtab.html#c:21"><span class="id" title="variable">c</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a><br/>
<a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssreflect.html#::boolean_if_scope:'if'_x_'then'_x_'else'_x"><span class="id" title="notation">if</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">(</span></a><a class="idref" href="Combi.Combi.stdtab.html#r:20"><span class="id" title="variable">r</span></a> <span class="id" title="notation">==</span> <a class="idref" href="Combi.Combi.stdtab.html#i:19"><span class="id" title="variable">i</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">)</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">(</span></a><a class="idref" href="Combi.Combi.stdtab.html#c:21"><span class="id" title="variable">c</span></a> <span class="id" title="notation">==</span> <span class="id" title="definition">nth</span> 0 (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:17"><span class="id" title="variable">t</span></a>) <a class="idref" href="Combi.Combi.stdtab.html#i:19"><span class="id" title="variable">i</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">)</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssreflect.html#::boolean_if_scope:'if'_x_'then'_x_'else'_x"><span class="id" title="notation">then</span></a> <a class="idref" href="Combi.Combi.stdtab.html#l:18"><span class="id" title="variable">l</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssreflect.html#::boolean_if_scope:'if'_x_'then'_x_'else'_x"><span class="id" title="notation">else</span></a> <a class="idref" href="Combi.Combi.tableau.html#get_tab"><span class="id" title="definition">get_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:17"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="Combi.Combi.stdtab.html#r:20"><span class="id" title="variable">r</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="Combi.Combi.stdtab.html#c:21"><span class="id" title="variable">c</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a>.<br/>
<br/>
</div>
<div class="doc">
<a id="lab86"></a><h2 class="section">Finding the largest entry</h2>
</div>
<div class="code">
<span class="id" title="keyword">Fixpoint</span> <a id="last_big" class="idref" href="#last_big"><span class="id" title="definition">last_big</span></a> <a id="t:22" class="idref" href="#t:22"><span class="id" title="binder">t</span></a> <a id="b:23" class="idref" href="#b:23"><span class="id" title="binder">b</span></a> :=<br/>
<span class="id" title="keyword">if</span> <a class="idref" href="Combi.Combi.stdtab.html#t:22"><span class="id" title="variable">t</span></a> <span class="id" title="keyword">is</span> <span class="id" title="var">t0</span> <span class="id" title="notation">::</span> <span class="id" title="var">t'</span> <span class="id" title="keyword">then</span><br/>
<a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssreflect.html#::boolean_if_scope:'if'_x_'then'_x_'else'_x"><span class="id" title="notation">if</span></a> <span class="id" title="definition">last</span> <a class="idref" href="Combi.Combi.stdtab.html#b:23"><span class="id" title="variable">b</span></a> <span class="id" title="var">t0</span> <span class="id" title="notation">==</span> <a class="idref" href="Combi.Combi.stdtab.html#b:23"><span class="id" title="variable">b</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssreflect.html#::boolean_if_scope:'if'_x_'then'_x_'else'_x"><span class="id" title="notation">then</span></a> 0<br/>
<a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssreflect.html#::boolean_if_scope:'if'_x_'then'_x_'else'_x"><span class="id" title="notation">else</span></a> <span class="id" title="notation">(</span><a class="idref" href="Combi.Combi.stdtab.html#last_big:24"><span class="id" title="definition">last_big</span></a> <span class="id" title="var">t'</span> <a class="idref" href="Combi.Combi.stdtab.html#b:23"><span class="id" title="variable">b</span></a><span class="id" title="notation">).+1</span><br/>
<span class="id" title="keyword">else</span> 0.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="allLeq_to_word_hd" class="idref" href="#allLeq_to_word_hd"><span class="id" title="lemma">allLeq_to_word_hd</span></a> <a id="r:26" class="idref" href="#r:26"><span class="id" title="binder">r</span></a> <a id="t:27" class="idref" href="#t:27"><span class="id" title="binder">t</span></a> <a id="b:28" class="idref" href="#b:28"><span class="id" title="binder">b</span></a> : <a class="idref" href="Combi.Basic.ordtype.html#allLeq"><span class="id" title="definition">allLeq</span></a> (<a class="idref" href="Combi.Combi.tableau.html#to_word"><span class="id" title="definition">to_word</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#r:26"><span class="id" title="variable">r</span></a> <span class="id" title="notation">::</span> <a class="idref" href="Combi.Combi.stdtab.html#t:27"><span class="id" title="variable">t</span></a>)) <a class="idref" href="Combi.Combi.stdtab.html#b:28"><span class="id" title="variable">b</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Basic.ordtype.html#allLeq"><span class="id" title="definition">allLeq</span></a> <a class="idref" href="Combi.Combi.stdtab.html#r:26"><span class="id" title="variable">r</span></a> <a class="idref" href="Combi.Combi.stdtab.html#b:28"><span class="id" title="variable">b</span></a>.<br/>
<span class="id" title="keyword">Lemma</span> <a id="allLeq_to_word_tl" class="idref" href="#allLeq_to_word_tl"><span class="id" title="lemma">allLeq_to_word_tl</span></a> <a id="r:29" class="idref" href="#r:29"><span class="id" title="binder">r</span></a> <a id="t:30" class="idref" href="#t:30"><span class="id" title="binder">t</span></a> <a id="b:31" class="idref" href="#b:31"><span class="id" title="binder">b</span></a> : <a class="idref" href="Combi.Basic.ordtype.html#allLeq"><span class="id" title="definition">allLeq</span></a> (<a class="idref" href="Combi.Combi.tableau.html#to_word"><span class="id" title="definition">to_word</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#r:29"><span class="id" title="variable">r</span></a> <span class="id" title="notation">::</span> <a class="idref" href="Combi.Combi.stdtab.html#t:30"><span class="id" title="variable">t</span></a>)) <a class="idref" href="Combi.Combi.stdtab.html#b:31"><span class="id" title="variable">b</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Basic.ordtype.html#allLeq"><span class="id" title="definition">allLeq</span></a> (<a class="idref" href="Combi.Combi.tableau.html#to_word"><span class="id" title="definition">to_word</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:30"><span class="id" title="variable">t</span></a>) <a class="idref" href="Combi.Combi.stdtab.html#b:31"><span class="id" title="variable">b</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="last_bigP" class="idref" href="#last_bigP"><span class="id" title="lemma">last_bigP</span></a> <a id="t:32" class="idref" href="#t:32"><span class="id" title="binder">t</span></a> <a id="b:33" class="idref" href="#b:33"><span class="id" title="binder">b</span></a> <a id="i:34" class="idref" href="#i:34"><span class="id" title="binder">i</span></a> :<br/>
<a class="idref" href="Combi.Combi.tableau.html#is_tableau"><span class="id" title="definition">is_tableau</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:32"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Basic.ordtype.html#allLeq"><span class="id" title="definition">allLeq</span></a> (<a class="idref" href="Combi.Combi.tableau.html#to_word"><span class="id" title="definition">to_word</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:32"><span class="id" title="variable">t</span></a>) <a class="idref" href="Combi.Combi.stdtab.html#b:33"><span class="id" title="variable">b</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#reflect"><span class="id" title="inductive">reflect</span></a> (<span class="id" title="definition">last</span> <a class="idref" href="Combi.Combi.stdtab.html#b:33"><span class="id" title="variable">b</span></a> (<span class="id" title="definition">nth</span> <span class="id" title="notation">[::]</span> <a class="idref" href="Combi.Combi.stdtab.html#t:32"><span class="id" title="variable">t</span></a> <a class="idref" href="Combi.Combi.stdtab.html#i:34"><span class="id" title="variable">i</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#b:33"><span class="id" title="variable">b</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">/\</span></a><br/>
<span class="id" title="keyword">forall</span> <a id="j:35" class="idref" href="#j:35"><span class="id" title="binder">j</span></a>, <a class="idref" href="Combi.Combi.stdtab.html#j:35"><span class="id" title="variable">j</span></a> <span class="id" title="notation"><</span> <a class="idref" href="Combi.Combi.stdtab.html#i:34"><span class="id" title="variable">i</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> (<span class="id" title="definition">last</span> <a class="idref" href="Combi.Combi.stdtab.html#b:33"><span class="id" title="variable">b</span></a> (<span class="id" title="definition">nth</span> <span class="id" title="notation">[::]</span> <a class="idref" href="Combi.Combi.stdtab.html#t:32"><span class="id" title="variable">t</span></a> <a class="idref" href="Combi.Combi.stdtab.html#j:35"><span class="id" title="variable">j</span></a>) <span class="id" title="notation"><</span> <a class="idref" href="Combi.Combi.stdtab.html#b:33"><span class="id" title="variable">b</span></a>)%<span class="id" title="var">O</span>)<br/>
(<a class="idref" href="Combi.Combi.stdtab.html#i:34"><span class="id" title="variable">i</span></a> <span class="id" title="notation">==</span> <a class="idref" href="Combi.Combi.stdtab.html#last_big"><span class="id" title="definition">last_big</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:32"><span class="id" title="variable">t</span></a> <a class="idref" href="Combi.Combi.stdtab.html#b:33"><span class="id" title="variable">b</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="last_big_append_nth" class="idref" href="#last_big_append_nth"><span class="id" title="lemma">last_big_append_nth</span></a> <a id="t:36" class="idref" href="#t:36"><span class="id" title="binder">t</span></a> <a id="b:37" class="idref" href="#b:37"><span class="id" title="binder">b</span></a> <a id="lb:38" class="idref" href="#lb:38"><span class="id" title="binder">lb</span></a> :<br/>
<a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">(</span></a><span class="id" title="keyword">forall</span> <a id="j:39" class="idref" href="#j:39"><span class="id" title="binder">j</span></a> : <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>, <a class="idref" href="Combi.Combi.stdtab.html#j:39"><span class="id" title="variable">j</span></a> <span class="id" title="notation"><</span> <a class="idref" href="Combi.Combi.stdtab.html#lb:38"><span class="id" title="variable">lb</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> (<span class="id" title="definition">last</span> <a class="idref" href="Combi.Combi.stdtab.html#b:37"><span class="id" title="variable">b</span></a> (<span class="id" title="definition">nth</span> <span class="id" title="notation">[::]</span> <a class="idref" href="Combi.Combi.stdtab.html#t:36"><span class="id" title="variable">t</span></a> <a class="idref" href="Combi.Combi.stdtab.html#j:39"><span class="id" title="variable">j</span></a>) <span class="id" title="notation"><</span> <a class="idref" href="Combi.Combi.stdtab.html#b:37"><span class="id" title="variable">b</span></a>)%<span class="id" title="var">O</span><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">)</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<a class="idref" href="Combi.Combi.stdtab.html#last_big"><span class="id" title="definition">last_big</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#append_nth"><span class="id" title="definition">append_nth</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:36"><span class="id" title="variable">t</span></a> <a class="idref" href="Combi.Combi.stdtab.html#b:37"><span class="id" title="variable">b</span></a> <a class="idref" href="Combi.Combi.stdtab.html#lb:38"><span class="id" title="variable">lb</span></a>) <a class="idref" href="Combi.Combi.stdtab.html#b:37"><span class="id" title="variable">b</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#lb:38"><span class="id" title="variable">lb</span></a>.<br/>
<br/>
<span class="id" title="keyword">End</span> <a class="idref" href="Combi.Combi.stdtab.html#AppendNth"><span class="id" title="section">AppendNth</span></a>.<br/>
<br/>
</div>
<div class="doc">
<a id="lab87"></a><h1 class="section">Bijection standard tableau <-> Yamanouchi words</h1>
</div>
<div class="code">
<span class="id" title="keyword">Section</span> <a id="Bijection" class="idref" href="#Bijection"><span class="id" title="section">Bijection</span></a>.<br/>
<br/>
<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Type</span> <span class="id" title="var">y</span> : <span class="id" title="abbreviation">seq</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>.<br/>
<span class="id" title="keyword">Implicit</span> <span class="id" title="keyword">Types</span> <span class="id" title="var">t</span> : <span class="id" title="abbreviation">seq</span> (<span class="id" title="abbreviation">seq</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>).<br/>
<br/>
<span class="id" title="keyword">Definition</span> <a id="is_stdtab" class="idref" href="#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a id="t:40" class="idref" href="#t:40"><span class="id" title="binder">t</span></a> := <a class="idref" href="Combi.Combi.tableau.html#is_tableau"><span class="id" title="definition">is_tableau</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:40"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">&&</span></a> <a class="idref" href="Combi.Combi.std.html#is_std"><span class="id" title="definition">is_std</span></a> (<a class="idref" href="Combi.Combi.tableau.html#to_word"><span class="id" title="definition">to_word</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:40"><span class="id" title="variable">t</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="stdtabP" class="idref" href="#stdtabP"><span class="id" title="lemma">stdtabP</span></a> <a id="t:41" class="idref" href="#t:41"><span class="id" title="binder">t</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:41"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.tableau.html#is_tableau"><span class="id" title="definition">is_tableau</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:41"><span class="id" title="variable">t</span></a>.<br/>
<br/>
<span class="id" title="keyword">Fixpoint</span> <a id="stdtab_of_yam" class="idref" href="#stdtab_of_yam"><span class="id" title="definition">stdtab_of_yam</span></a> <a id="y:42" class="idref" href="#y:42"><span class="id" title="binder">y</span></a> :=<br/>
<span class="id" title="keyword">if</span> <a class="idref" href="Combi.Combi.stdtab.html#y:42"><span class="id" title="variable">y</span></a> <span class="id" title="keyword">is</span> <span class="id" title="var">y0</span> <span class="id" title="notation">::</span> <span class="id" title="var">y'</span> <span class="id" title="keyword">then</span><br/>
<a class="idref" href="Combi.Combi.stdtab.html#append_nth"><span class="id" title="definition">append_nth</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#stdtab_of_yam:43"><span class="id" title="definition">stdtab_of_yam</span></a> <span class="id" title="var">y'</span>) (<span class="id" title="definition">size</span> <span class="id" title="var">y'</span>) <span class="id" title="var">y0</span><br/>
<span class="id" title="keyword">else</span> <span class="id" title="notation">[::]</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="shape_stdtab_of_yam" class="idref" href="#shape_stdtab_of_yam"><span class="id" title="lemma">shape_stdtab_of_yam</span></a> <a id="y:45" class="idref" href="#y:45"><span class="id" title="binder">y</span></a> : <span class="id" title="definition">shape</span> (<a class="idref" href="Combi.Combi.stdtab.html#stdtab_of_yam"><span class="id" title="definition">stdtab_of_yam</span></a> <a class="idref" href="Combi.Combi.stdtab.html#y:45"><span class="id" title="variable">y</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.Yamanouchi.html#evalseq"><span class="id" title="definition">evalseq</span></a> <a class="idref" href="Combi.Combi.stdtab.html#y:45"><span class="id" title="variable">y</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="size_stdtab_of_yam" class="idref" href="#size_stdtab_of_yam"><span class="id" title="lemma">size_stdtab_of_yam</span></a> <a id="y:46" class="idref" href="#y:46"><span class="id" title="binder">y</span></a> : <a class="idref" href="Combi.Combi.tableau.html#size_tab"><span class="id" title="definition">size_tab</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#stdtab_of_yam"><span class="id" title="definition">stdtab_of_yam</span></a> <a class="idref" href="Combi.Combi.stdtab.html#y:46"><span class="id" title="variable">y</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <span class="id" title="definition">size</span> <a class="idref" href="Combi.Combi.stdtab.html#y:46"><span class="id" title="variable">y</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="std_of_yam" class="idref" href="#std_of_yam"><span class="id" title="lemma">std_of_yam</span></a> <a id="y:47" class="idref" href="#y:47"><span class="id" title="binder">y</span></a> : <a class="idref" href="Combi.Combi.std.html#is_std"><span class="id" title="definition">is_std</span></a> (<a class="idref" href="Combi.Combi.tableau.html#to_word"><span class="id" title="definition">to_word</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#stdtab_of_yam"><span class="id" title="definition">stdtab_of_yam</span></a> <a class="idref" href="Combi.Combi.stdtab.html#y:47"><span class="id" title="variable">y</span></a>)).<br/>
<br/>
</div>
<div class="doc">
The following proof is an experiment to see if proof using get_tab are
easier than proof by induction on the structure of tableaux
</div>
<div class="code">
<span class="id" title="keyword">Lemma</span> <a id="is_tab_append_nth_size_alternative_proof" class="idref" href="#is_tab_append_nth_size_alternative_proof"><span class="id" title="lemma">is_tab_append_nth_size_alternative_proof</span></a> <a id="r:48" class="idref" href="#r:48"><span class="id" title="binder">r</span></a> <a id="T:49" class="idref" href="#T:49"><span class="id" title="binder">T</span></a> <a id="n:50" class="idref" href="#n:50"><span class="id" title="binder">n</span></a> :<br/>
<span class="id" title="definition">all</span> (<span class="id" title="definition">gtn</span> <a class="idref" href="Combi.Combi.stdtab.html#n:50"><span class="id" title="variable">n</span></a>) (<a class="idref" href="Combi.Combi.tableau.html#to_word"><span class="id" title="definition">to_word</span></a> <a class="idref" href="Combi.Combi.stdtab.html#T:49"><span class="id" title="variable">T</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<a class="idref" href="Combi.Combi.partition.html#is_part"><span class="id" title="definition">is_part</span></a> (<span class="id" title="definition">incr_nth</span> (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#T:49"><span class="id" title="variable">T</span></a>) <a class="idref" href="Combi.Combi.stdtab.html#r:48"><span class="id" title="variable">r</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<a class="idref" href="Combi.Combi.tableau.html#is_tableau"><span class="id" title="definition">is_tableau</span></a> <a class="idref" href="Combi.Combi.stdtab.html#T:49"><span class="id" title="variable">T</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.tableau.html#is_tableau"><span class="id" title="definition">is_tableau</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#append_nth"><span class="id" title="definition">append_nth</span></a> <a class="idref" href="Combi.Combi.stdtab.html#T:49"><span class="id" title="variable">T</span></a> <a class="idref" href="Combi.Combi.stdtab.html#n:50"><span class="id" title="variable">n</span></a> <a class="idref" href="Combi.Combi.stdtab.html#r:48"><span class="id" title="variable">r</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="is_tab_append_nth_size" class="idref" href="#is_tab_append_nth_size"><span class="id" title="lemma">is_tab_append_nth_size</span></a> <a id="r:52" class="idref" href="#r:52"><span class="id" title="binder">r</span></a> <a id="T:53" class="idref" href="#T:53"><span class="id" title="binder">T</span></a> <a id="n:54" class="idref" href="#n:54"><span class="id" title="binder">n</span></a> :<br/>
<span class="id" title="definition">all</span> (<span class="id" title="definition">gtn</span> <a class="idref" href="Combi.Combi.stdtab.html#n:54"><span class="id" title="variable">n</span></a>) (<a class="idref" href="Combi.Combi.tableau.html#to_word"><span class="id" title="definition">to_word</span></a> <a class="idref" href="Combi.Combi.stdtab.html#T:53"><span class="id" title="variable">T</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<a class="idref" href="Combi.Combi.partition.html#is_part"><span class="id" title="definition">is_part</span></a> (<span class="id" title="definition">incr_nth</span> (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#T:53"><span class="id" title="variable">T</span></a>) <a class="idref" href="Combi.Combi.stdtab.html#r:52"><span class="id" title="variable">r</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<a class="idref" href="Combi.Combi.tableau.html#is_tableau"><span class="id" title="definition">is_tableau</span></a> <a class="idref" href="Combi.Combi.stdtab.html#T:53"><span class="id" title="variable">T</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.tableau.html#is_tableau"><span class="id" title="definition">is_tableau</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#append_nth"><span class="id" title="definition">append_nth</span></a> <a class="idref" href="Combi.Combi.stdtab.html#T:53"><span class="id" title="variable">T</span></a> <a class="idref" href="Combi.Combi.stdtab.html#n:54"><span class="id" title="variable">n</span></a> <a class="idref" href="Combi.Combi.stdtab.html#r:52"><span class="id" title="variable">r</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="stdtab_of_yamP" class="idref" href="#stdtab_of_yamP"><span class="id" title="lemma">stdtab_of_yamP</span></a> <a id="y:55" class="idref" href="#y:55"><span class="id" title="binder">y</span></a> : <a class="idref" href="Combi.Combi.Yamanouchi.html#is_yam"><span class="id" title="definition">is_yam</span></a> <a class="idref" href="Combi.Combi.stdtab.html#y:55"><span class="id" title="variable">y</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#stdtab_of_yam"><span class="id" title="definition">stdtab_of_yam</span></a> <a class="idref" href="Combi.Combi.stdtab.html#y:55"><span class="id" title="variable">y</span></a>).<br/>
<br/>
<span class="id" title="keyword">Section</span> <a id="Bijection.StdTabInd" class="idref" href="#Bijection.StdTabInd"><span class="id" title="section">StdTabInd</span></a>.<br/>
<br/>
<span class="id" title="keyword">Fixpoint</span> <a id="remn_rec" class="idref" href="#remn_rec"><span class="id" title="definition">remn_rec</span></a> <a id="t:56" class="idref" href="#t:56"><span class="id" title="binder">t</span></a> <a id="n:57" class="idref" href="#n:57"><span class="id" title="binder">n</span></a> :=<br/>
<span class="id" title="keyword">if</span> <a class="idref" href="Combi.Combi.stdtab.html#t:56"><span class="id" title="variable">t</span></a> <span class="id" title="keyword">is</span> <span class="id" title="var">t0</span> <span class="id" title="notation">::</span> <span class="id" title="var">t'</span> <span class="id" title="keyword">then</span><br/>
<span class="id" title="keyword">match</span> <span class="id" title="var">t0</span> <span class="id" title="keyword">with</span><br/>
| <span class="id" title="notation">[::]</span> => <span class="id" title="notation">[::]</span> <br/>
| <span class="id" title="var">l0</span> <span class="id" title="notation">::</span> <span class="id" title="var">t0'</span> => <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssreflect.html#::boolean_if_scope:'if'_x_'then'_x_'else'_x"><span class="id" title="notation">if</span></a> <span class="id" title="definition">last</span> <span class="id" title="var">l0</span> <span class="id" title="var">t0'</span> <span class="id" title="notation">==</span> <a class="idref" href="Combi.Combi.stdtab.html#n:57"><span class="id" title="variable">n</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssreflect.html#::boolean_if_scope:'if'_x_'then'_x_'else'_x"><span class="id" title="notation">then</span></a><br/>
<a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssreflect.html#::boolean_if_scope:'if'_x_'then'_x_'else'_x"><span class="id" title="notation">if</span></a> <span class="id" title="var">t0'</span> <span class="id" title="notation">==</span> <span class="id" title="notation">[::]</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssreflect.html#::boolean_if_scope:'if'_x_'then'_x_'else'_x"><span class="id" title="notation">then</span></a> <span class="id" title="notation">[::]</span><br/>
<a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssreflect.html#::boolean_if_scope:'if'_x_'then'_x_'else'_x"><span class="id" title="notation">else</span></a> <span class="id" title="notation">(</span><span class="id" title="definition">belast</span> <span class="id" title="var">l0</span> <span class="id" title="var">t0'</span><span class="id" title="notation">)</span> <span class="id" title="notation">::</span> <span class="id" title="var">t'</span><br/>
<a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssreflect.html#::boolean_if_scope:'if'_x_'then'_x_'else'_x"><span class="id" title="notation">else</span></a> <span class="id" title="var">t0</span> <span class="id" title="notation">::</span> <a class="idref" href="Combi.Combi.stdtab.html#remn_rec:58"><span class="id" title="definition">remn_rec</span></a> <span class="id" title="var">t'</span> <a class="idref" href="Combi.Combi.stdtab.html#n:57"><span class="id" title="variable">n</span></a><br/>
<span class="id" title="keyword">end</span><br/>
<span class="id" title="keyword">else</span> <span class="id" title="notation">[::]</span> .<br/>
<span class="id" title="keyword">Definition</span> <a id="remn" class="idref" href="#remn"><span class="id" title="definition">remn</span></a> <a id="t:61" class="idref" href="#t:61"><span class="id" title="binder">t</span></a> := <a class="idref" href="Combi.Combi.stdtab.html#remn_rec"><span class="id" title="definition">remn_rec</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:61"><span class="id" title="variable">t</span></a> <span class="id" title="notation">(</span><a class="idref" href="Combi.Combi.tableau.html#size_tab"><span class="id" title="definition">size_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:61"><span class="id" title="variable">t</span></a><span class="id" title="notation">).-1</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="remnP" class="idref" href="#remnP"><span class="id" title="lemma">remnP</span></a> <a id="t:62" class="idref" href="#t:62"><span class="id" title="binder">t</span></a> :<br/>
<a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:62"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:62"><span class="id" title="variable">t</span></a> <span class="id" title="notation">!=</span> <span class="id" title="notation">[::]</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<a class="idref" href="Combi.Combi.tableau.html#is_tableau"><span class="id" title="definition">is_tableau</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#remn"><span class="id" title="definition">remn</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:62"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#ba2b0e492d2b4675a0acf3ea92aabadd"><span class="id" title="notation">/\</span></a><br/>
<a class="idref" href="Combi.Combi.stdtab.html#append_nth"><span class="id" title="definition">append_nth</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#remn"><span class="id" title="definition">remn</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:62"><span class="id" title="variable">t</span></a>) <span class="id" title="notation">(</span><a class="idref" href="Combi.Combi.tableau.html#size_tab"><span class="id" title="definition">size_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:62"><span class="id" title="variable">t</span></a><span class="id" title="notation">).-1</span> (<a class="idref" href="Combi.Combi.stdtab.html#last_big"><span class="id" title="definition">last_big</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:62"><span class="id" title="variable">t</span></a> <span class="id" title="notation">(</span><a class="idref" href="Combi.Combi.tableau.html#size_tab"><span class="id" title="definition">size_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:62"><span class="id" title="variable">t</span></a><span class="id" title="notation">).-1</span>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:62"><span class="id" title="variable">t</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="is_stdtab_remn" class="idref" href="#is_stdtab_remn"><span class="id" title="lemma">is_stdtab_remn</span></a> <a id="t:63" class="idref" href="#t:63"><span class="id" title="binder">t</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:63"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#remn"><span class="id" title="definition">remn</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:63"><span class="id" title="variable">t</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="append_nth_remn" class="idref" href="#append_nth_remn"><span class="id" title="lemma">append_nth_remn</span></a> <a id="t:64" class="idref" href="#t:64"><span class="id" title="binder">t</span></a> :<br/>
<a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:64"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:64"><span class="id" title="variable">t</span></a> <span class="id" title="notation">!=</span> <span class="id" title="notation">[::]</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<a class="idref" href="Combi.Combi.stdtab.html#append_nth"><span class="id" title="definition">append_nth</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#remn"><span class="id" title="definition">remn</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:64"><span class="id" title="variable">t</span></a>) <span class="id" title="notation">(</span><a class="idref" href="Combi.Combi.tableau.html#size_tab"><span class="id" title="definition">size_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:64"><span class="id" title="variable">t</span></a><span class="id" title="notation">).-1</span> (<a class="idref" href="Combi.Combi.stdtab.html#last_big"><span class="id" title="definition">last_big</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:64"><span class="id" title="variable">t</span></a> <span class="id" title="notation">(</span><a class="idref" href="Combi.Combi.tableau.html#size_tab"><span class="id" title="definition">size_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:64"><span class="id" title="variable">t</span></a><span class="id" title="notation">).-1</span>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:64"><span class="id" title="variable">t</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="size_tab_remn" class="idref" href="#size_tab_remn"><span class="id" title="lemma">size_tab_remn</span></a> <a id="t:65" class="idref" href="#t:65"><span class="id" title="binder">t</span></a> :<br/>
<a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:65"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:65"><span class="id" title="variable">t</span></a> <span class="id" title="notation">!=</span> <span class="id" title="notation">[::]</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.tableau.html#size_tab"><span class="id" title="definition">size_tab</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#remn"><span class="id" title="definition">remn</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:65"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <span class="id" title="notation">(</span><a class="idref" href="Combi.Combi.tableau.html#size_tab"><span class="id" title="definition">size_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:65"><span class="id" title="variable">t</span></a><span class="id" title="notation">).-1</span>.<br/>
<br/>
<span class="id" title="keyword">End</span> <a class="idref" href="Combi.Combi.stdtab.html#Bijection.StdTabInd"><span class="id" title="section">StdTabInd</span></a>.<br/>
<br/>
<span class="id" title="keyword">Fixpoint</span> <a id="yam_of_stdtab_rec" class="idref" href="#yam_of_stdtab_rec"><span class="id" title="definition">yam_of_stdtab_rec</span></a> <a id="n:66" class="idref" href="#n:66"><span class="id" title="binder">n</span></a> <a id="t:67" class="idref" href="#t:67"><span class="id" title="binder">t</span></a> :=<br/>
<span class="id" title="keyword">if</span> <a class="idref" href="Combi.Combi.stdtab.html#n:66"><span class="id" title="variable">n</span></a> <span class="id" title="keyword">is</span> <span class="id" title="var">n'</span><span class="id" title="notation">.+1</span> <span class="id" title="keyword">then</span><br/>
<span class="id" title="notation">(</span><a class="idref" href="Combi.Combi.stdtab.html#last_big"><span class="id" title="definition">last_big</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:67"><span class="id" title="variable">t</span></a> <span class="id" title="var">n'</span><span class="id" title="notation">)</span> <span class="id" title="notation">::</span> <a class="idref" href="Combi.Combi.stdtab.html#yam_of_stdtab_rec:68"><span class="id" title="definition">yam_of_stdtab_rec</span></a> <span class="id" title="var">n'</span> (<a class="idref" href="Combi.Combi.stdtab.html#remn"><span class="id" title="definition">remn</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:67"><span class="id" title="variable">t</span></a>)<br/>
<span class="id" title="keyword">else</span> <span class="id" title="notation">[::]</span>.<br/>
<span class="id" title="keyword">Definition</span> <a id="yam_of_stdtab" class="idref" href="#yam_of_stdtab"><span class="id" title="definition">yam_of_stdtab</span></a> <a id="t:70" class="idref" href="#t:70"><span class="id" title="binder">t</span></a> := <a class="idref" href="Combi.Combi.stdtab.html#yam_of_stdtab_rec"><span class="id" title="definition">yam_of_stdtab_rec</span></a> (<a class="idref" href="Combi.Combi.tableau.html#size_tab"><span class="id" title="definition">size_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:70"><span class="id" title="variable">t</span></a>) <a class="idref" href="Combi.Combi.stdtab.html#t:70"><span class="id" title="variable">t</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="size_yam_of_stdtab_rec" class="idref" href="#size_yam_of_stdtab_rec"><span class="id" title="lemma">size_yam_of_stdtab_rec</span></a> <a id="n:71" class="idref" href="#n:71"><span class="id" title="binder">n</span></a> <a id="t:72" class="idref" href="#t:72"><span class="id" title="binder">t</span></a> : <span class="id" title="definition">size</span> (<a class="idref" href="Combi.Combi.stdtab.html#yam_of_stdtab_rec"><span class="id" title="definition">yam_of_stdtab_rec</span></a> <a class="idref" href="Combi.Combi.stdtab.html#n:71"><span class="id" title="variable">n</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:72"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#n:71"><span class="id" title="variable">n</span></a>.<br/>
<br/>
<span class="id" title="keyword">Theorem</span> <a id="yam_of_stdtabK" class="idref" href="#yam_of_stdtabK"><span class="id" title="lemma">yam_of_stdtabK</span></a> <a id="t:73" class="idref" href="#t:73"><span class="id" title="binder">t</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:73"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.stdtab.html#stdtab_of_yam"><span class="id" title="definition">stdtab_of_yam</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#yam_of_stdtab"><span class="id" title="definition">yam_of_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:73"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:73"><span class="id" title="variable">t</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="find_append_nth" class="idref" href="#find_append_nth"><span class="id" title="lemma">find_append_nth</span></a> (<a id="l:74" class="idref" href="#l:74"><span class="id" title="binder">l</span></a> : <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) <a id="t:75" class="idref" href="#t:75"><span class="id" title="binder">t</span></a> <a id="r:76" class="idref" href="#r:76"><span class="id" title="binder">r</span></a> :<br/>
<a class="idref" href="Combi.Combi.stdtab.html#l:74"><span class="id" title="variable">l</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">(</span></a><a class="idref" href="Combi.Combi.tableau.html#to_word"><span class="id" title="definition">to_word</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:75"><span class="id" title="variable">t</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<span class="id" title="definition">find</span> (<span class="id" title="keyword">fun</span> <a id="x:77" class="idref" href="#x:77"><span class="id" title="binder">x</span></a> : <span class="id" title="abbreviation">seq</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a> => <a class="idref" href="Combi.Combi.stdtab.html#l:74"><span class="id" title="variable">l</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">\</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#b09457274bcb94927e289b8a9e9cd3f7"><span class="id" title="notation">in</span></a> <a class="idref" href="Combi.Combi.stdtab.html#x:77"><span class="id" title="variable">x</span></a>) (<a class="idref" href="Combi.Combi.stdtab.html#append_nth"><span class="id" title="definition">append_nth</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:75"><span class="id" title="variable">t</span></a> <a class="idref" href="Combi.Combi.stdtab.html#l:74"><span class="id" title="variable">l</span></a> <a class="idref" href="Combi.Combi.stdtab.html#r:76"><span class="id" title="variable">r</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#r:76"><span class="id" title="variable">r</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="size_notin_stdtab_of_yam" class="idref" href="#size_notin_stdtab_of_yam"><span class="id" title="lemma">size_notin_stdtab_of_yam</span></a> <a id="y:78" class="idref" href="#y:78"><span class="id" title="binder">y</span></a> : <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">(</span></a><span class="id" title="definition">size</span> <a class="idref" href="Combi.Combi.stdtab.html#y:78"><span class="id" title="variable">y</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">)</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">(</span></a><a class="idref" href="Combi.Combi.tableau.html#to_word"><span class="id" title="definition">to_word</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#stdtab_of_yam"><span class="id" title="definition">stdtab_of_yam</span></a> <a class="idref" href="Combi.Combi.stdtab.html#y:78"><span class="id" title="variable">y</span></a>)<a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">)</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="incr_nth_injl" class="idref" href="#incr_nth_injl"><span class="id" title="lemma">incr_nth_injl</span></a> <a id="u:79" class="idref" href="#u:79"><span class="id" title="binder">u</span></a> <a id="v:80" class="idref" href="#v:80"><span class="id" title="binder">v</span></a> <a id="i:81" class="idref" href="#i:81"><span class="id" title="binder">i</span></a> :<br/>
0 <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="Combi.Combi.stdtab.html#u:79"><span class="id" title="variable">u</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> 0 <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="Combi.Combi.stdtab.html#v:80"><span class="id" title="variable">v</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <span class="id" title="definition">incr_nth</span> <a class="idref" href="Combi.Combi.stdtab.html#u:79"><span class="id" title="variable">u</span></a> <a class="idref" href="Combi.Combi.stdtab.html#i:81"><span class="id" title="variable">i</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <span class="id" title="definition">incr_nth</span> <a class="idref" href="Combi.Combi.stdtab.html#v:80"><span class="id" title="variable">v</span></a> <a class="idref" href="Combi.Combi.stdtab.html#i:81"><span class="id" title="variable">i</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.stdtab.html#u:79"><span class="id" title="variable">u</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#v:80"><span class="id" title="variable">v</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="shape0" class="idref" href="#shape0"><span class="id" title="lemma">shape0</span></a> <a id="d:82" class="idref" href="#d:82"><span class="id" title="binder">d</span></a> (<a id="T:83" class="idref" href="#T:83"><span class="id" title="binder">T</span></a> : <span class="id" title="abbreviation">orderType</span> <a class="idref" href="Combi.Combi.stdtab.html#d:82"><span class="id" title="variable">d</span></a>) (<a id="u:84" class="idref" href="#u:84"><span class="id" title="binder">u</span></a> : <span class="id" title="abbreviation">seq</span> (<span class="id" title="abbreviation">seq</span> <a class="idref" href="Combi.Combi.stdtab.html#T:83"><span class="id" title="variable">T</span></a>)) :<br/>
<span class="id" title="notation">[::]</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="Combi.Combi.stdtab.html#u:84"><span class="id" title="variable">u</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> 0 <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">(</span></a><span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#u:84"><span class="id" title="variable">u</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">)</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="append_nth_injl" class="idref" href="#append_nth_injl"><span class="id" title="lemma">append_nth_injl</span></a> <a id="d:85" class="idref" href="#d:85"><span class="id" title="binder">d</span></a> (<a id="T:86" class="idref" href="#T:86"><span class="id" title="binder">T</span></a> : <a class="idref" href="Combi.Basic.ordtype.html#InhOrder.Exports.inhOrderType"><span class="id" title="abbreviation">inhOrderType</span></a> <a class="idref" href="Combi.Combi.stdtab.html#d:85"><span class="id" title="variable">d</span></a>) (<a id="u:87" class="idref" href="#u:87"><span class="id" title="binder">u</span></a> <a id="v:88" class="idref" href="#v:88"><span class="id" title="binder">v</span></a> : <span class="id" title="abbreviation">seq</span> (<span class="id" title="abbreviation">seq</span> <a class="idref" href="Combi.Combi.stdtab.html#T:86"><span class="id" title="variable">T</span></a>)) (<a id="l:89" class="idref" href="#l:89"><span class="id" title="binder">l</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#T:86"><span class="id" title="variable">T</span></a>) <a id="p:90" class="idref" href="#p:90"><span class="id" title="binder">p</span></a> :<br/>
<span class="id" title="notation">[::]</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="Combi.Combi.stdtab.html#u:87"><span class="id" title="variable">u</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <span class="id" title="notation">[::]</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="Combi.Combi.stdtab.html#v:88"><span class="id" title="variable">v</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<a class="idref" href="Combi.Combi.stdtab.html#append_nth"><span class="id" title="definition">append_nth</span></a> <a class="idref" href="Combi.Combi.stdtab.html#u:87"><span class="id" title="variable">u</span></a> <a class="idref" href="Combi.Combi.stdtab.html#l:89"><span class="id" title="variable">l</span></a> <a class="idref" href="Combi.Combi.stdtab.html#p:90"><span class="id" title="variable">p</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#append_nth"><span class="id" title="definition">append_nth</span></a> <a class="idref" href="Combi.Combi.stdtab.html#v:88"><span class="id" title="variable">v</span></a> <a class="idref" href="Combi.Combi.stdtab.html#l:89"><span class="id" title="variable">l</span></a> <a class="idref" href="Combi.Combi.stdtab.html#p:90"><span class="id" title="variable">p</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.stdtab.html#u:87"><span class="id" title="variable">u</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#v:88"><span class="id" title="variable">v</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="stdtab_of_yam_nil" class="idref" href="#stdtab_of_yam_nil"><span class="id" title="lemma">stdtab_of_yam_nil</span></a> <a id="y:91" class="idref" href="#y:91"><span class="id" title="binder">y</span></a> : <a class="idref" href="Combi.Combi.Yamanouchi.html#is_yam"><span class="id" title="definition">is_yam</span></a> <a class="idref" href="Combi.Combi.stdtab.html#y:91"><span class="id" title="variable">y</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <span class="id" title="notation">[::]</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">\</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">notin</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">(</span></a><a class="idref" href="Combi.Combi.stdtab.html#stdtab_of_yam"><span class="id" title="definition">stdtab_of_yam</span></a> <a class="idref" href="Combi.Combi.stdtab.html#y:91"><span class="id" title="variable">y</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#c1ad6bcc76a6221225111f87bc3b0c3d"><span class="id" title="notation">)</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="stdtab_of_yam_inj" class="idref" href="#stdtab_of_yam_inj"><span class="id" title="lemma">stdtab_of_yam_inj</span></a> <a id="x:92" class="idref" href="#x:92"><span class="id" title="binder">x</span></a> <a id="y:93" class="idref" href="#y:93"><span class="id" title="binder">y</span></a> :<br/>
<a class="idref" href="Combi.Combi.Yamanouchi.html#is_yam"><span class="id" title="definition">is_yam</span></a> <a class="idref" href="Combi.Combi.stdtab.html#x:92"><span class="id" title="variable">x</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.Yamanouchi.html#is_yam"><span class="id" title="definition">is_yam</span></a> <a class="idref" href="Combi.Combi.stdtab.html#y:93"><span class="id" title="variable">y</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.stdtab.html#stdtab_of_yam"><span class="id" title="definition">stdtab_of_yam</span></a> <a class="idref" href="Combi.Combi.stdtab.html#x:92"><span class="id" title="variable">x</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#stdtab_of_yam"><span class="id" title="definition">stdtab_of_yam</span></a> <a class="idref" href="Combi.Combi.stdtab.html#y:93"><span class="id" title="variable">y</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.stdtab.html#x:92"><span class="id" title="variable">x</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#y:93"><span class="id" title="variable">y</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="shape_yam_of_stdtab" class="idref" href="#shape_yam_of_stdtab"><span class="id" title="lemma">shape_yam_of_stdtab</span></a> <a id="t:95" class="idref" href="#t:95"><span class="id" title="binder">t</span></a> :<br/>
<a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:95"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.Yamanouchi.html#evalseq"><span class="id" title="definition">evalseq</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#yam_of_stdtab"><span class="id" title="definition">yam_of_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:95"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:95"><span class="id" title="variable">t</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="size_yam_of_stdtab" class="idref" href="#size_yam_of_stdtab"><span class="id" title="lemma">size_yam_of_stdtab</span></a> <a id="t:96" class="idref" href="#t:96"><span class="id" title="binder">t</span></a> :<br/>
<a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:96"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <span class="id" title="definition">size</span> (<a class="idref" href="Combi.Combi.stdtab.html#yam_of_stdtab"><span class="id" title="definition">yam_of_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:96"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.tableau.html#size_tab"><span class="id" title="definition">size_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:96"><span class="id" title="variable">t</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="part_yam_of_stdtab" class="idref" href="#part_yam_of_stdtab"><span class="id" title="lemma">part_yam_of_stdtab</span></a> <a id="t:97" class="idref" href="#t:97"><span class="id" title="binder">t</span></a> :<br/>
<a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:97"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.partition.html#is_part"><span class="id" title="definition">is_part</span></a> (<a class="idref" href="Combi.Combi.Yamanouchi.html#evalseq"><span class="id" title="definition">evalseq</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#yam_of_stdtab"><span class="id" title="definition">yam_of_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:97"><span class="id" title="variable">t</span></a>)).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="yam_of_stdtabP" class="idref" href="#yam_of_stdtabP"><span class="id" title="lemma">yam_of_stdtabP</span></a> <a id="t:98" class="idref" href="#t:98"><span class="id" title="binder">t</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:98"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.Yamanouchi.html#is_yam"><span class="id" title="definition">is_yam</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#yam_of_stdtab"><span class="id" title="definition">yam_of_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:98"><span class="id" title="variable">t</span></a>).<br/>
<br/>
<span class="id" title="keyword">Theorem</span> <a id="stdtab_of_yamK" class="idref" href="#stdtab_of_yamK"><span class="id" title="lemma">stdtab_of_yamK</span></a> <a id="y:99" class="idref" href="#y:99"><span class="id" title="binder">y</span></a> : <a class="idref" href="Combi.Combi.Yamanouchi.html#is_yam"><span class="id" title="definition">is_yam</span></a> <a class="idref" href="Combi.Combi.stdtab.html#y:99"><span class="id" title="variable">y</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.stdtab.html#yam_of_stdtab"><span class="id" title="definition">yam_of_stdtab</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#stdtab_of_yam"><span class="id" title="definition">stdtab_of_yam</span></a> <a class="idref" href="Combi.Combi.stdtab.html#y:99"><span class="id" title="variable">y</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#y:99"><span class="id" title="variable">y</span></a>.<br/>
<br/>
<span class="id" title="keyword">End</span> <a class="idref" href="Combi.Combi.stdtab.html#Bijection"><span class="id" title="section">Bijection</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="eq_inv_is_row" class="idref" href="#eq_inv_is_row"><span class="id" title="lemma">eq_inv_is_row</span></a> <a id="d1:100" class="idref" href="#d1:100"><span class="id" title="binder">d1</span></a> <a id="d2:101" class="idref" href="#d2:101"><span class="id" title="binder">d2</span></a> (<a id="T1:102" class="idref" href="#T1:102"><span class="id" title="binder">T1</span></a> : <a class="idref" href="Combi.Basic.ordtype.html#InhOrder.Exports.inhOrderType"><span class="id" title="abbreviation">inhOrderType</span></a> <a class="idref" href="Combi.Combi.stdtab.html#d1:100"><span class="id" title="variable">d1</span></a>) (<a id="T2:103" class="idref" href="#T2:103"><span class="id" title="binder">T2</span></a> : <a class="idref" href="Combi.Basic.ordtype.html#InhOrder.Exports.inhOrderType"><span class="id" title="abbreviation">inhOrderType</span></a> <a class="idref" href="Combi.Combi.stdtab.html#d2:101"><span class="id" title="variable">d2</span></a>)<br/>
(<a id="u1:104" class="idref" href="#u1:104"><span class="id" title="binder">u1</span></a> : <span class="id" title="abbreviation">seq</span> <a class="idref" href="Combi.Combi.stdtab.html#T1:102"><span class="id" title="variable">T1</span></a>) (<a id="u2:105" class="idref" href="#u2:105"><span class="id" title="binder">u2</span></a> : <span class="id" title="abbreviation">seq</span> <a class="idref" href="Combi.Combi.stdtab.html#T2:103"><span class="id" title="variable">T2</span></a>) :<br/>
<a class="idref" href="Combi.Combi.std.html#eq_inv"><span class="id" title="definition">eq_inv</span></a> <a class="idref" href="Combi.Combi.stdtab.html#u1:104"><span class="id" title="variable">u1</span></a> <a class="idref" href="Combi.Combi.stdtab.html#u2:105"><span class="id" title="variable">u2</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.tableau.html#is_row"><span class="id" title="abbreviation">is_row</span></a> <a class="idref" href="Combi.Combi.stdtab.html#u1:104"><span class="id" title="variable">u1</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.tableau.html#is_row"><span class="id" title="abbreviation">is_row</span></a> <a class="idref" href="Combi.Combi.stdtab.html#u2:105"><span class="id" title="variable">u2</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="is_row_stdE" class="idref" href="#is_row_stdE"><span class="id" title="lemma">is_row_stdE</span></a> <a id="d:106" class="idref" href="#d:106"><span class="id" title="binder">d</span></a> (<a id="T:107" class="idref" href="#T:107"><span class="id" title="binder">T</span></a> : <a class="idref" href="Combi.Basic.ordtype.html#InhOrder.Exports.inhOrderType"><span class="id" title="abbreviation">inhOrderType</span></a> <a class="idref" href="Combi.Combi.stdtab.html#d:106"><span class="id" title="variable">d</span></a>) (<a id="w:108" class="idref" href="#w:108"><span class="id" title="binder">w</span></a> : <span class="id" title="abbreviation">seq</span> <a class="idref" href="Combi.Combi.stdtab.html#T:107"><span class="id" title="variable">T</span></a>) :<br/>
<a class="idref" href="Combi.Combi.tableau.html#is_row"><span class="id" title="abbreviation">is_row</span></a> (<a class="idref" href="Combi.Combi.std.html#std"><span class="id" title="definition">std</span></a> <a class="idref" href="Combi.Combi.stdtab.html#w:108"><span class="id" title="variable">w</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.tableau.html#is_row"><span class="id" title="abbreviation">is_row</span></a> <a class="idref" href="Combi.Combi.stdtab.html#w:108"><span class="id" title="variable">w</span></a>.<br/>
<br/>
</div>
<div class="doc">
<a id="lab88"></a><h1 class="section">Sigma type for standard tableaux</h1>
</div>
<div class="code">
<span class="id" title="keyword">Section</span> <a id="StdtabOfShape" class="idref" href="#StdtabOfShape"><span class="id" title="section">StdtabOfShape</span></a>.<br/>
<br/>
<span class="id" title="keyword">Definition</span> <a id="is_stdtab_of_shape" class="idref" href="#is_stdtab_of_shape"><span class="id" title="definition">is_stdtab_of_shape</span></a> <a id="sh:109" class="idref" href="#sh:109"><span class="id" title="binder">sh</span></a> := <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#10dd1f0b03819efd5777bd139f7faec4"><span class="id" title="notation">[</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#10dd1f0b03819efd5777bd139f7faec4"><span class="id" title="notation">pred</span></a> <a id="t:110" class="idref" href="#t:110"><span class="id" title="binder">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#10dd1f0b03819efd5777bd139f7faec4"><span class="id" title="notation">|</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">(</span></a><a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:110"><span class="id" title="variable">t</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">)</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">(</span></a><span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:110"><span class="id" title="variable">t</span></a> <span class="id" title="notation">==</span> <a class="idref" href="Combi.Combi.stdtab.html#sh:109"><span class="id" title="variable">sh</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">)</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#10dd1f0b03819efd5777bd139f7faec4"><span class="id" title="notation">]</span></a>.<br/>
<span class="id" title="keyword">Definition</span> <a id="enum_stdtabsh" class="idref" href="#enum_stdtabsh"><span class="id" title="definition">enum_stdtabsh</span></a> <a id="sh:111" class="idref" href="#sh:111"><span class="id" title="binder">sh</span></a> : <span class="id" title="abbreviation">seq</span> (<span class="id" title="abbreviation">seq</span> (<span class="id" title="abbreviation">seq</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>)) :=<br/>
<span class="id" title="definition">map</span> <a class="idref" href="Combi.Combi.stdtab.html#stdtab_of_yam"><span class="id" title="definition">stdtab_of_yam</span></a> (<a class="idref" href="Combi.Combi.Yamanouchi.html#enum_yameval"><span class="id" title="definition">enum_yameval</span></a> <a class="idref" href="Combi.Combi.stdtab.html#sh:111"><span class="id" title="variable">sh</span></a>).<br/>
<br/>
<span class="id" title="keyword">Variable</span> <a id="StdtabOfShape.sh" class="idref" href="#StdtabOfShape.sh"><span class="id" title="variable">sh</span></a> : <a class="idref" href="Combi.Combi.partition.html#intpart"><span class="id" title="record">intpart</span></a>.<br/>
<br/>
<span class="id" title="keyword">Structure</span> <a id="stdtabsh" class="idref" href="#stdtabsh"><span class="id" title="record">stdtabsh</span></a> : <span class="id" title="keyword">Set</span> :=<br/>
<span class="id" title="var">StdtabSh</span> {<br/>
<a id="stdtabshval" class="idref" href="#stdtabshval"><span class="id" title="projection">stdtabshval</span></a> :> <span class="id" title="abbreviation">seq</span> (<span class="id" title="abbreviation">seq</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>);<br/>
<span class="id" title="var">_</span> : <a class="idref" href="Combi.Combi.stdtab.html#is_stdtab_of_shape"><span class="id" title="definition">is_stdtab_of_shape</span></a> <a class="idref" href="Combi.Combi.stdtab.html#StdtabOfShape.sh"><span class="id" title="variable">sh</span></a> <a class="idref" href="Combi.Combi.stdtab.html#stdtabshval:115"><span class="id" title="method">stdtabshval</span></a><br/>
}.<br/>
<br/>
<span class="id" title="keyword">Let</span> <a id="StdtabOfShape.stdtabsh_enum" class="idref" href="#StdtabOfShape.stdtabsh_enum"><span class="id" title="variable">stdtabsh_enum</span></a> : <span class="id" title="abbreviation">seq</span> <a class="idref" href="Combi.Combi.stdtab.html#stdtabsh"><span class="id" title="record">stdtabsh</span></a> := <span class="id" title="definition">pmap</span> <span class="id" title="definition">insub</span> (<a class="idref" href="Combi.Combi.stdtab.html#enum_stdtabsh"><span class="id" title="definition">enum_stdtabsh</span></a> <a class="idref" href="Combi.Combi.stdtab.html#StdtabOfShape.sh"><span class="id" title="variable">sh</span></a>).<br/>
<br/>
<span class="id" title="keyword">Fact</span> <a id="finite_stdtabsh" class="idref" href="#finite_stdtabsh"><span class="id" title="lemma">finite_stdtabsh</span></a> : <span class="id" title="abbreviation">Finite.axiom</span> <a class="idref" href="Combi.Combi.stdtab.html#StdtabOfShape.stdtabsh_enum"><span class="id" title="variable">stdtabsh_enum</span></a>.<br/>
<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="stdtabshP" class="idref" href="#stdtabshP"><span class="id" title="lemma">stdtabshP</span></a> (<a id="t:116" class="idref" href="#t:116"><span class="id" title="binder">t</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#stdtabsh"><span class="id" title="record">stdtabsh</span></a>) : <a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:116"><span class="id" title="variable">t</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="shape_stdtabsh" class="idref" href="#shape_stdtabsh"><span class="id" title="lemma">shape_stdtabsh</span></a> (<a id="t:117" class="idref" href="#t:117"><span class="id" title="binder">t</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#stdtabsh"><span class="id" title="record">stdtabsh</span></a>) : <span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:117"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#StdtabOfShape.sh"><span class="id" title="variable">sh</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="enum_stdtabshE" class="idref" href="#enum_stdtabshE"><span class="id" title="lemma">enum_stdtabshE</span></a> : <span class="id" title="definition">map</span> <span class="id" title="abbreviation">val</span> (<span class="id" title="abbreviation">enum</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#fa3b33ae9d0a52de608b305a09f3b881"><span class="id" title="notation">{:</span></a> <a class="idref" href="Combi.Combi.stdtab.html#stdtabsh"><span class="id" title="record">stdtabsh</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#fa3b33ae9d0a52de608b305a09f3b881"><span class="id" title="notation">}</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#enum_stdtabsh"><span class="id" title="definition">enum_stdtabsh</span></a> <a class="idref" href="Combi.Combi.stdtab.html#StdtabOfShape.sh"><span class="id" title="variable">sh</span></a>.<br/>
<br/>
<span class="id" title="keyword">Fact</span> <a id="hyper_stdtabsh_subproof" class="idref" href="#hyper_stdtabsh_subproof"><span class="id" title="lemma">hyper_stdtabsh_subproof</span></a> :<br/>
<a class="idref" href="Combi.Combi.stdtab.html#is_stdtab_of_shape"><span class="id" title="definition">is_stdtab_of_shape</span></a> <a class="idref" href="Combi.Combi.stdtab.html#StdtabOfShape.sh"><span class="id" title="variable">sh</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#stdtab_of_yam"><span class="id" title="definition">stdtab_of_yam</span></a> (<a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssreflect.html#locked"><span class="id" title="definition">locked</span></a> (<a class="idref" href="Combi.Combi.Yamanouchi.html#hyper_yameval"><span class="id" title="definition">hyper_yameval</span></a> <a class="idref" href="Combi.Combi.stdtab.html#StdtabOfShape.sh"><span class="id" title="variable">sh</span></a>))).<br/>
<span class="id" title="keyword">Definition</span> <a id="hyper_stdtabsh" class="idref" href="#hyper_stdtabsh"><span class="id" title="definition">hyper_stdtabsh</span></a> := <a class="idref" href="Combi.Combi.stdtab.html#StdtabSh"><span class="id" title="constructor">StdtabSh</span></a> <a class="idref" href="Combi.Combi.stdtab.html#hyper_stdtabsh_subproof"><span class="id" title="lemma">hyper_stdtabsh_subproof</span></a>.<br/>
<br/>
<span class="id" title="keyword">End</span> <a class="idref" href="Combi.Combi.stdtab.html#StdtabOfShape"><span class="id" title="section">StdtabOfShape</span></a>.<br/>
#[<span class="id" title="var">export</span>] <span class="id" title="keyword">Hint</span> <span class="id" title="keyword">Resolve</span> <span class="id" title="var">stdtabshP</span> : <span class="id" title="var">core</span>.<br/>
<br/>
<span class="id" title="keyword">Section</span> <a id="StdtabCombClass" class="idref" href="#StdtabCombClass"><span class="id" title="section">StdtabCombClass</span></a>.<br/>
<br/>
<span class="id" title="keyword">Variable</span> <a id="StdtabCombClass.n" class="idref" href="#StdtabCombClass.n"><span class="id" title="variable">n</span></a> : <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>.<br/>
<br/>
<span class="id" title="keyword">Definition</span> <a id="is_stdtab_of_n" class="idref" href="#is_stdtab_of_n"><span class="id" title="definition">is_stdtab_of_n</span></a> := <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#10dd1f0b03819efd5777bd139f7faec4"><span class="id" title="notation">[</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#10dd1f0b03819efd5777bd139f7faec4"><span class="id" title="notation">pred</span></a> <a id="t:120" class="idref" href="#t:120"><span class="id" title="binder">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#10dd1f0b03819efd5777bd139f7faec4"><span class="id" title="notation">|</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">(</span></a><a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:120"><span class="id" title="variable">t</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">)</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">&&</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">(</span></a><a class="idref" href="Combi.Combi.tableau.html#size_tab"><span class="id" title="definition">size_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:120"><span class="id" title="variable">t</span></a> <span class="id" title="notation">==</span> <a class="idref" href="Combi.Combi.stdtab.html#StdtabCombClass.n"><span class="id" title="variable">n</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#::bool_scope:x_'&&'_x"><span class="id" title="notation">)</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#10dd1f0b03819efd5777bd139f7faec4"><span class="id" title="notation">]</span></a>.<br/>
<br/>
<span class="id" title="keyword">Structure</span> <a id="stdtabn" class="idref" href="#stdtabn"><span class="id" title="record">stdtabn</span></a> : <span class="id" title="keyword">Set</span> :=<br/>
<span class="id" title="var">StdtabN</span> {<a id="stdtabnval" class="idref" href="#stdtabnval"><span class="id" title="projection">stdtabnval</span></a> :> <span class="id" title="abbreviation">seq</span> (<span class="id" title="abbreviation">seq</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>); <span class="id" title="var">_</span> : <a class="idref" href="Combi.Combi.stdtab.html#is_stdtab_of_n"><span class="id" title="definition">is_stdtab_of_n</span></a> <a class="idref" href="Combi.Combi.stdtab.html#stdtabnval:122"><span class="id" title="method">stdtabnval</span></a>}.<br/>
<br/>
<span class="id" title="keyword">Definition</span> <a id="enum_stdtabn" class="idref" href="#enum_stdtabn"><span class="id" title="definition">enum_stdtabn</span></a> : <span class="id" title="abbreviation">seq</span> (<span class="id" title="abbreviation">seq</span> (<span class="id" title="abbreviation">seq</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>)) :=<br/>
<span class="id" title="definition">map</span> (<a class="idref" href="Combi.Combi.stdtab.html#stdtab_of_yam"><span class="id" title="definition">stdtab_of_yam</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrfun.html#687e14754dadb7c0b04f27d8f71d2638"><span class="id" title="notation">\</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrfun.html#687e14754dadb7c0b04f27d8f71d2638"><span class="id" title="notation">o</span></a> <span class="id" title="abbreviation">val</span>) (<span class="id" title="abbreviation">enum</span> (<a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#fa3b33ae9d0a52de608b305a09f3b881"><span class="id" title="notation">{:</span></a> <a class="idref" href="Combi.Combi.Yamanouchi.html#yamn"><span class="id" title="record">yamn</span></a> <a class="idref" href="Combi.Combi.stdtab.html#StdtabCombClass.n"><span class="id" title="variable">n</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#fa3b33ae9d0a52de608b305a09f3b881"><span class="id" title="notation">}</span></a>)).<br/>
<span class="id" title="keyword">Let</span> <a id="StdtabCombClass.stdtabn_enum" class="idref" href="#StdtabCombClass.stdtabn_enum"><span class="id" title="variable">stdtabn_enum</span></a> : <span class="id" title="abbreviation">seq</span> <a class="idref" href="Combi.Combi.stdtab.html#stdtabn"><span class="id" title="record">stdtabn</span></a> := <span class="id" title="definition">pmap</span> <span class="id" title="definition">insub</span> <a class="idref" href="Combi.Combi.stdtab.html#enum_stdtabn"><span class="id" title="definition">enum_stdtabn</span></a>.<br/>
<br/>
<span class="id" title="keyword">Fact</span> <a id="finite_stdtabn" class="idref" href="#finite_stdtabn"><span class="id" title="lemma">finite_stdtabn</span></a> : <span class="id" title="abbreviation">Finite.axiom</span> <a class="idref" href="Combi.Combi.stdtab.html#StdtabCombClass.stdtabn_enum"><span class="id" title="variable">stdtabn_enum</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="stdtabnP" class="idref" href="#stdtabnP"><span class="id" title="lemma">stdtabnP</span></a> (<a id="s:123" class="idref" href="#s:123"><span class="id" title="binder">s</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#stdtabn"><span class="id" title="record">stdtabn</span></a>) : <a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#s:123"><span class="id" title="variable">s</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="size_tab_stdtabn" class="idref" href="#size_tab_stdtabn"><span class="id" title="lemma">size_tab_stdtabn</span></a> (<a id="s:124" class="idref" href="#s:124"><span class="id" title="binder">s</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#stdtabn"><span class="id" title="record">stdtabn</span></a>) : <a class="idref" href="Combi.Combi.tableau.html#size_tab"><span class="id" title="definition">size_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#s:124"><span class="id" title="variable">s</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#StdtabCombClass.n"><span class="id" title="variable">n</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="sumn_shape_stdtabnE" class="idref" href="#sumn_shape_stdtabnE"><span class="id" title="lemma">sumn_shape_stdtabnE</span></a> (<a id="Q:125" class="idref" href="#Q:125"><span class="id" title="binder">Q</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#stdtabn"><span class="id" title="record">stdtabn</span></a>) : <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">(</span></a><span class="id" title="definition">sumn</span> (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#Q:125"><span class="id" title="variable">Q</span></a>)<a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">)</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#StdtabCombClass.n"><span class="id" title="variable">n</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="is_part_shape_deg" class="idref" href="#is_part_shape_deg"><span class="id" title="lemma">is_part_shape_deg</span></a> (<a id="Q:126" class="idref" href="#Q:126"><span class="id" title="binder">Q</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#stdtabn"><span class="id" title="record">stdtabn</span></a>) : <a class="idref" href="Combi.Combi.partition.html#is_part_of_n"><span class="id" title="definition">is_part_of_n</span></a> <a class="idref" href="Combi.Combi.stdtab.html#StdtabCombClass.n"><span class="id" title="variable">n</span></a> (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#Q:126"><span class="id" title="variable">Q</span></a>).<br/>
<span class="id" title="keyword">Definition</span> <a id="shape_deg" class="idref" href="#shape_deg"><span class="id" title="definition">shape_deg</span></a> (<a id="Q:127" class="idref" href="#Q:127"><span class="id" title="binder">Q</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#stdtabn"><span class="id" title="record">stdtabn</span></a>) := <a class="idref" href="Combi.Combi.partition.html#IntPartN"><span class="id" title="constructor">IntPartN</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#is_part_shape_deg"><span class="id" title="lemma">is_part_shape_deg</span></a> <a class="idref" href="Combi.Combi.stdtab.html#Q:127"><span class="id" title="variable">Q</span></a>).<br/>
<br/>
<span class="id" title="keyword">End</span> <a class="idref" href="Combi.Combi.stdtab.html#StdtabCombClass"><span class="id" title="section">StdtabCombClass</span></a>.<br/>
<br/>
<span class="id" title="keyword">Section</span> <a id="StdtabnOfStdtabsh" class="idref" href="#StdtabnOfStdtabsh"><span class="id" title="section">StdtabnOfStdtabsh</span></a>.<br/>
<br/>
<span class="id" title="keyword">Variables</span> (<a id="StdtabnOfStdtabsh.n" class="idref" href="#StdtabnOfStdtabsh.n"><span class="id" title="variable">n</span></a> : <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) (<a id="StdtabnOfStdtabsh.sh" class="idref" href="#StdtabnOfStdtabsh.sh"><span class="id" title="variable">sh</span></a> : <a class="idref" href="Combi.Combi.partition.html#intpartn"><span class="id" title="record">intpartn</span></a> <a class="idref" href="Combi.Combi.stdtab.html#n:129"><span class="id" title="variable">n</span></a>).<br/>
<br/>
<span class="id" title="keyword">Fact</span> <a id="stdtabn_of_sh_subproof" class="idref" href="#stdtabn_of_sh_subproof"><span class="id" title="lemma">stdtabn_of_sh_subproof</span></a> (<a id="t:132" class="idref" href="#t:132"><span class="id" title="binder">t</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#stdtabsh"><span class="id" title="record">stdtabsh</span></a> <a class="idref" href="Combi.Combi.stdtab.html#StdtabnOfStdtabsh.sh"><span class="id" title="variable">sh</span></a>) : <a class="idref" href="Combi.Combi.stdtab.html#is_stdtab_of_n"><span class="id" title="definition">is_stdtab_of_n</span></a> <a class="idref" href="Combi.Combi.stdtab.html#StdtabnOfStdtabsh.n"><span class="id" title="variable">n</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:132"><span class="id" title="variable">t</span></a>.<br/>
<span class="id" title="keyword">Definition</span> <a id="stdtabn_of_sh" class="idref" href="#stdtabn_of_sh"><span class="id" title="definition">stdtabn_of_sh</span></a> <a id="t:133" class="idref" href="#t:133"><span class="id" title="binder">t</span></a> := <a class="idref" href="Combi.Combi.stdtab.html#StdtabN"><span class="id" title="constructor">StdtabN</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#stdtabn_of_sh_subproof"><span class="id" title="lemma">stdtabn_of_sh_subproof</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:133"><span class="id" title="variable">t</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="shape_deg_stdtabn_of_sh" class="idref" href="#shape_deg_stdtabn_of_sh"><span class="id" title="lemma">shape_deg_stdtabn_of_sh</span></a> <a id="t:134" class="idref" href="#t:134"><span class="id" title="binder">t</span></a> :<br/>
<a class="idref" href="Combi.Combi.stdtab.html#shape_deg"><span class="id" title="definition">shape_deg</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#stdtabn_of_sh"><span class="id" title="definition">stdtabn_of_sh</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:134"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#StdtabnOfStdtabsh.sh"><span class="id" title="variable">sh</span></a>.<br/>
<br/>
<span class="id" title="keyword">End</span> <a class="idref" href="Combi.Combi.stdtab.html#StdtabnOfStdtabsh"><span class="id" title="section">StdtabnOfStdtabsh</span></a>.<br/>
<br/>
</div>
<div class="doc">
<a id="lab89"></a><h1 class="section">Conjugate of a standard tableau</h1>
</div>
<div class="code">
<span class="id" title="keyword">Section</span> <a id="ConjTab" class="idref" href="#ConjTab"><span class="id" title="section">ConjTab</span></a>.<br/>
<br/>
<span class="id" title="keyword">Variables</span> (<a id="ConjTab.disp" class="idref" href="#ConjTab.disp"><span class="id" title="variable">disp</span></a>: <span class="id" title="var">_</span>) (<a id="ConjTab.T" class="idref" href="#ConjTab.T"><span class="id" title="variable">T</span></a> : <a class="idref" href="Combi.Basic.ordtype.html#InhOrder.Exports.inhOrderType"><span class="id" title="abbreviation">inhOrderType</span></a> <a class="idref" href="Combi.Combi.stdtab.html#disp:136"><span class="id" title="variable">disp</span></a>).<br/>
<br/>
<span class="id" title="keyword">Definition</span> <a id="conj_tab" class="idref" href="#conj_tab"><span class="id" title="definition">conj_tab</span></a> (<a id="t:139" class="idref" href="#t:139"><span class="id" title="binder">t</span></a> : <span class="id" title="abbreviation">seq</span> (<span class="id" title="abbreviation">seq</span> <a class="idref" href="Combi.Combi.stdtab.html#ConjTab.T"><span class="id" title="variable">T</span></a>)) : <span class="id" title="abbreviation">seq</span> (<span class="id" title="abbreviation">seq</span> <a class="idref" href="Combi.Combi.stdtab.html#ConjTab.T"><span class="id" title="variable">T</span></a>) :=<br/>
<span class="id" title="keyword">let</span> <a id="c:140" class="idref" href="#c:140"><span class="id" title="binder">c</span></a> := <a class="idref" href="Combi.Combi.partition.html#conj_part"><span class="id" title="definition">conj_part</span></a> (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:139"><span class="id" title="variable">t</span></a>) <span class="id" title="tactic">in</span><br/>
<span class="id" title="definition">mkseq</span> (<span class="id" title="keyword">fun</span> <a id="i:141" class="idref" href="#i:141"><span class="id" title="binder">i</span></a> => <span class="id" title="definition">mkseq</span> (<span class="id" title="keyword">fun</span> <a id="j:142" class="idref" href="#j:142"><span class="id" title="binder">j</span></a> => <a class="idref" href="Combi.Combi.tableau.html#get_tab"><span class="id" title="definition">get_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:139"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="Combi.Combi.stdtab.html#j:142"><span class="id" title="variable">j</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="Combi.Combi.stdtab.html#i:141"><span class="id" title="variable">i</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a>) (<span class="id" title="definition">nth</span> 0 <a class="idref" href="Combi.Combi.stdtab.html#c:140"><span class="id" title="variable">c</span></a> <a class="idref" href="Combi.Combi.stdtab.html#i:141"><span class="id" title="variable">i</span></a>)) (<span class="id" title="definition">size</span> <a class="idref" href="Combi.Combi.stdtab.html#c:140"><span class="id" title="variable">c</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="size_conj_tab" class="idref" href="#size_conj_tab"><span class="id" title="lemma">size_conj_tab</span></a> <a id="t:143" class="idref" href="#t:143"><span class="id" title="binder">t</span></a> : <span class="id" title="definition">size</span> (<a class="idref" href="Combi.Combi.stdtab.html#conj_tab"><span class="id" title="definition">conj_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:143"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <span class="id" title="definition">size</span> (<a class="idref" href="Combi.Combi.partition.html#conj_part"><span class="id" title="definition">conj_part</span></a> (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:143"><span class="id" title="variable">t</span></a>)).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="shape_conj_tab" class="idref" href="#shape_conj_tab"><span class="id" title="lemma">shape_conj_tab</span></a> <a id="t:144" class="idref" href="#t:144"><span class="id" title="binder">t</span></a> : <span class="id" title="definition">shape</span> (<a class="idref" href="Combi.Combi.stdtab.html#conj_tab"><span class="id" title="definition">conj_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:144"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.partition.html#conj_part"><span class="id" title="definition">conj_part</span></a> (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:144"><span class="id" title="variable">t</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="get_conj_tab" class="idref" href="#get_conj_tab"><span class="id" title="lemma">get_conj_tab</span></a> <a id="t:154" class="idref" href="#t:154"><span class="id" title="binder">t</span></a> :<br/>
<a class="idref" href="Combi.Combi.partition.html#is_part"><span class="id" title="definition">is_part</span></a> (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:154"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<span class="id" title="keyword">forall</span> <a id="i:155" class="idref" href="#i:155"><span class="id" title="binder">i</span></a> <a id="j:156" class="idref" href="#j:156"><span class="id" title="binder">j</span></a>, <a class="idref" href="Combi.Combi.tableau.html#get_tab"><span class="id" title="definition">get_tab</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#conj_tab"><span class="id" title="definition">conj_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:154"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="Combi.Combi.stdtab.html#i:155"><span class="id" title="variable">i</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="Combi.Combi.stdtab.html#j:156"><span class="id" title="variable">j</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.tableau.html#get_tab"><span class="id" title="definition">get_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:154"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">(</span></a><a class="idref" href="Combi.Combi.stdtab.html#j:156"><span class="id" title="variable">j</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">,</span></a> <a class="idref" href="Combi.Combi.stdtab.html#i:155"><span class="id" title="variable">i</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Datatypes.html#e6756e10c36f149b18b4a8741ed83079"><span class="id" title="notation">)</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="eq_from_shape_get_tab" class="idref" href="#eq_from_shape_get_tab"><span class="id" title="lemma">eq_from_shape_get_tab</span></a> (<a id="t:157" class="idref" href="#t:157"><span class="id" title="binder">t</span></a> <a id="u:158" class="idref" href="#u:158"><span class="id" title="binder">u</span></a> : <span class="id" title="abbreviation">seq</span> (<span class="id" title="abbreviation">seq</span> <a class="idref" href="Combi.Combi.stdtab.html#ConjTab.T"><span class="id" title="variable">T</span></a>)) :<br/>
<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:157"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#u:158"><span class="id" title="variable">u</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.tableau.html#get_tab"><span class="id" title="definition">get_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:157"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrfun.html#44b19bd81f7a1388073ea8a65e6fa993"><span class="id" title="notation">=1</span></a> <a class="idref" href="Combi.Combi.tableau.html#get_tab"><span class="id" title="definition">get_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#u:158"><span class="id" title="variable">u</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:157"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#u:158"><span class="id" title="variable">u</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="conj_tab_shapeK" class="idref" href="#conj_tab_shapeK"><span class="id" title="lemma">conj_tab_shapeK</span></a> <a id="t:159" class="idref" href="#t:159"><span class="id" title="binder">t</span></a> : <a class="idref" href="Combi.Combi.partition.html#is_part"><span class="id" title="definition">is_part</span></a> (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:159"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.stdtab.html#conj_tab"><span class="id" title="definition">conj_tab</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#conj_tab"><span class="id" title="definition">conj_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:159"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:159"><span class="id" title="variable">t</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="conj_tabK" class="idref" href="#conj_tabK"><span class="id" title="lemma">conj_tabK</span></a> <a id="t:160" class="idref" href="#t:160"><span class="id" title="binder">t</span></a> : <a class="idref" href="Combi.Combi.tableau.html#is_tableau"><span class="id" title="definition">is_tableau</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:160"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.stdtab.html#conj_tab"><span class="id" title="definition">conj_tab</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#conj_tab"><span class="id" title="definition">conj_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:160"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:160"><span class="id" title="variable">t</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="append_nth_conj_tab" class="idref" href="#append_nth_conj_tab"><span class="id" title="lemma">append_nth_conj_tab</span></a> (<a id="t:161" class="idref" href="#t:161"><span class="id" title="binder">t</span></a> : <span class="id" title="abbreviation">seq</span> (<span class="id" title="abbreviation">seq</span> <a class="idref" href="Combi.Combi.stdtab.html#ConjTab.T"><span class="id" title="variable">T</span></a>)) <a id="l:162" class="idref" href="#l:162"><span class="id" title="binder">l</span></a> <a id="i:163" class="idref" href="#i:163"><span class="id" title="binder">i</span></a> :<br/>
<a class="idref" href="Combi.Combi.partition.html#is_part"><span class="id" title="definition">is_part</span></a> (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:161"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<a class="idref" href="Combi.Combi.partition.html#is_add_corner"><span class="id" title="definition">is_add_corner</span></a> (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:161"><span class="id" title="variable">t</span></a>) <a class="idref" href="Combi.Combi.stdtab.html#i:163"><span class="id" title="variable">i</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<a class="idref" href="Combi.Combi.stdtab.html#conj_tab"><span class="id" title="definition">conj_tab</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#append_nth"><span class="id" title="definition">append_nth</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:161"><span class="id" title="variable">t</span></a> <a class="idref" href="Combi.Combi.stdtab.html#l:162"><span class="id" title="variable">l</span></a> <a class="idref" href="Combi.Combi.stdtab.html#i:163"><span class="id" title="variable">i</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#append_nth"><span class="id" title="definition">append_nth</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#conj_tab"><span class="id" title="definition">conj_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:161"><span class="id" title="variable">t</span></a>) <a class="idref" href="Combi.Combi.stdtab.html#l:162"><span class="id" title="variable">l</span></a> (<span class="id" title="definition">nth</span> 0 (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:161"><span class="id" title="variable">t</span></a>) <a class="idref" href="Combi.Combi.stdtab.html#i:163"><span class="id" title="variable">i</span></a>).<br/>
<br/>
<span class="id" title="keyword">End</span> <a class="idref" href="Combi.Combi.stdtab.html#ConjTab"><span class="id" title="section">ConjTab</span></a>.<br/>
<br/>
<span class="id" title="keyword">Example</span> <a id="conj_tab_expl1" class="idref" href="#conj_tab_expl1"><span class="id" title="definition">conj_tab_expl1</span></a> :<br/>
<a class="idref" href="Combi.Combi.stdtab.html#conj_tab"><span class="id" title="definition">conj_tab</span></a> <span class="id" title="notation">[::</span> <span class="id" title="notation">[::</span> 0<span class="id" title="notation">;</span> 1<span class="id" title="notation">;</span> 4<span class="id" title="notation">];</span> <span class="id" title="notation">[::</span> 2<span class="id" title="notation">;</span> 3<span class="id" title="notation">]]</span> <span class="id" title="notation">==</span><br/>
<span class="id" title="notation">[::</span> <span class="id" title="notation">[::</span> 0<span class="id" title="notation">;</span> 2<span class="id" title="notation">];</span> <span class="id" title="notation">[::</span> 1<span class="id" title="notation">;</span> 3<span class="id" title="notation">];</span> <span class="id" title="notation">[::</span> 4<span class="id" title="notation">]</span><span class="id" title="notation">]</span>.<br/>
<span class="id" title="keyword">Example</span> <a id="conj_tab_expl2" class="idref" href="#conj_tab_expl2"><span class="id" title="definition">conj_tab_expl2</span></a> :<br/>
<a class="idref" href="Combi.Combi.stdtab.html#conj_tab"><span class="id" title="definition">conj_tab</span></a> <span class="id" title="notation">[::</span> <span class="id" title="notation">[::</span> 0<span class="id" title="notation">;</span> 1<span class="id" title="notation">;</span> 3<span class="id" title="notation">;</span> 4<span class="id" title="notation">];</span> <span class="id" title="notation">[::</span> 2<span class="id" title="notation">;</span> 5<span class="id" title="notation">];</span> <span class="id" title="notation">[::</span> 6<span class="id" title="notation">]</span><span class="id" title="notation">]</span> <span class="id" title="notation">==</span><br/>
<span class="id" title="notation">[::</span> <span class="id" title="notation">[::</span> 0<span class="id" title="notation">;</span> 2<span class="id" title="notation">;</span> 6<span class="id" title="notation">];</span> <span class="id" title="notation">[::</span> 1<span class="id" title="notation">;</span> 5<span class="id" title="notation">];</span> <span class="id" title="notation">[::</span> 3<span class="id" title="notation">]</span><span class="id" title="notation">;</span> <span class="id" title="notation">[::</span> 4<span class="id" title="notation">]</span><span class="id" title="notation">]</span>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="stdtab_get_tabNE" class="idref" href="#stdtab_get_tabNE"><span class="id" title="lemma">stdtab_get_tabNE</span></a> <a id="t:164" class="idref" href="#t:164"><span class="id" title="binder">t</span></a> :<br/>
<a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:164"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<span class="id" title="keyword">forall</span> <a id="rc1:165" class="idref" href="#rc1:165"><span class="id" title="binder">rc1</span></a> <a id="rc2:166" class="idref" href="#rc2:166"><span class="id" title="binder">rc2</span></a>,<br/>
<a class="idref" href="Combi.Combi.partition.html#in_shape"><span class="id" title="definition">in_shape</span></a> (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:164"><span class="id" title="variable">t</span></a>) <a class="idref" href="Combi.Combi.stdtab.html#rc1:165"><span class="id" title="variable">rc1</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<a class="idref" href="Combi.Combi.partition.html#in_shape"><span class="id" title="definition">in_shape</span></a> (<span class="id" title="definition">shape</span> <a class="idref" href="Combi.Combi.stdtab.html#t:164"><span class="id" title="variable">t</span></a>) <a class="idref" href="Combi.Combi.stdtab.html#rc2:166"><span class="id" title="variable">rc2</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a><br/>
<a class="idref" href="Combi.Combi.stdtab.html#rc1:165"><span class="id" title="variable">rc1</span></a> <span class="id" title="notation">!=</span> <a class="idref" href="Combi.Combi.stdtab.html#rc2:166"><span class="id" title="variable">rc2</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.tableau.html#get_tab"><span class="id" title="definition">get_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:164"><span class="id" title="variable">t</span></a> <a class="idref" href="Combi.Combi.stdtab.html#rc1:165"><span class="id" title="variable">rc1</span></a> <span class="id" title="notation">!=</span> <a class="idref" href="Combi.Combi.tableau.html#get_tab"><span class="id" title="definition">get_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:164"><span class="id" title="variable">t</span></a> <a class="idref" href="Combi.Combi.stdtab.html#rc2:166"><span class="id" title="variable">rc2</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="is_stdtab_conj" class="idref" href="#is_stdtab_conj"><span class="id" title="lemma">is_stdtab_conj</span></a> <a id="t:167" class="idref" href="#t:167"><span class="id" title="binder">t</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:167"><span class="id" title="variable">t</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#::type_scope:x_'->'_x"><span class="id" title="notation">-></span></a> <a class="idref" href="Combi.Combi.stdtab.html#is_stdtab"><span class="id" title="definition">is_stdtab</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#conj_tab"><span class="id" title="definition">conj_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:167"><span class="id" title="variable">t</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="conj_stdtabnP" class="idref" href="#conj_stdtabnP"><span class="id" title="lemma">conj_stdtabnP</span></a> <a id="n:168" class="idref" href="#n:168"><span class="id" title="binder">n</span></a> (<a id="t:169" class="idref" href="#t:169"><span class="id" title="binder">t</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#stdtabn"><span class="id" title="record">stdtabn</span></a> <a class="idref" href="Combi.Combi.stdtab.html#n:168"><span class="id" title="variable">n</span></a>):<br/>
<a class="idref" href="Combi.Combi.stdtab.html#is_stdtab_of_n"><span class="id" title="definition">is_stdtab_of_n</span></a> <a class="idref" href="Combi.Combi.stdtab.html#n:168"><span class="id" title="variable">n</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#conj_tab"><span class="id" title="definition">conj_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:169"><span class="id" title="variable">t</span></a>).<br/>
<span class="id" title="keyword">Canonical</span> <a id="conj_stdtabn" class="idref" href="#conj_stdtabn"><span class="id" title="definition">conj_stdtabn</span></a> <a id="n:170" class="idref" href="#n:170"><span class="id" title="binder">n</span></a> (<a id="t:171" class="idref" href="#t:171"><span class="id" title="binder">t</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#stdtabn"><span class="id" title="record">stdtabn</span></a> <a class="idref" href="Combi.Combi.stdtab.html#n:170"><span class="id" title="variable">n</span></a>) := <a class="idref" href="Combi.Combi.stdtab.html#StdtabN"><span class="id" title="constructor">StdtabN</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#conj_stdtabnP"><span class="id" title="lemma">conj_stdtabnP</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:171"><span class="id" title="variable">t</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="conj_stdtabshP" class="idref" href="#conj_stdtabshP"><span class="id" title="lemma">conj_stdtabshP</span></a> (<a id="sh:172" class="idref" href="#sh:172"><span class="id" title="binder">sh</span></a> : <a class="idref" href="Combi.Combi.partition.html#intpart"><span class="id" title="record">intpart</span></a>) (<a id="t:173" class="idref" href="#t:173"><span class="id" title="binder">t</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#stdtabsh"><span class="id" title="record">stdtabsh</span></a> <a class="idref" href="Combi.Combi.stdtab.html#sh:172"><span class="id" title="variable">sh</span></a>) :<br/>
<a class="idref" href="Combi.Combi.stdtab.html#is_stdtab_of_shape"><span class="id" title="definition">is_stdtab_of_shape</span></a> (<a class="idref" href="Combi.Combi.partition.html#conj_part"><span class="id" title="definition">conj_part</span></a> <a class="idref" href="Combi.Combi.stdtab.html#sh:172"><span class="id" title="variable">sh</span></a>) (<a class="idref" href="Combi.Combi.stdtab.html#conj_tab"><span class="id" title="definition">conj_tab</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:173"><span class="id" title="variable">t</span></a>).<br/>
<span class="id" title="keyword">Canonical</span> <a id="conj_stdtabsh" class="idref" href="#conj_stdtabsh"><span class="id" title="definition">conj_stdtabsh</span></a> {<a id="sh:174" class="idref" href="#sh:174"><span class="id" title="binder">sh</span></a> : <a class="idref" href="Combi.Combi.partition.html#intpart"><span class="id" title="record">intpart</span></a>} (<a id="t:175" class="idref" href="#t:175"><span class="id" title="binder">t</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#stdtabsh"><span class="id" title="record">stdtabsh</span></a> <a class="idref" href="Combi.Combi.stdtab.html#sh:174"><span class="id" title="variable">sh</span></a>) :=<br/>
<a class="idref" href="Combi.Combi.stdtab.html#StdtabSh"><span class="id" title="constructor">StdtabSh</span></a> (<a class="idref" href="Combi.Combi.stdtab.html#conj_stdtabshP"><span class="id" title="lemma">conj_stdtabshP</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:175"><span class="id" title="variable">t</span></a>).<br/>
<br/>
<span class="id" title="keyword">Definition</span> <a id="stdtabshcast" class="idref" href="#stdtabshcast"><span class="id" title="definition">stdtabshcast</span></a> <a id="m:176" class="idref" href="#m:176"><span class="id" title="binder">m</span></a> <a id="n:177" class="idref" href="#n:177"><span class="id" title="binder">n</span></a> (<a id="eq_mn:178" class="idref" href="#eq_mn:178"><span class="id" title="binder">eq_mn</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#m:176"><span class="id" title="variable">m</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#n:177"><span class="id" title="variable">n</span></a>) <a id="t:179" class="idref" href="#t:179"><span class="id" title="binder">t</span></a> :=<br/>
<span class="id" title="keyword">let</span>: <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrfun.html#erefl"><span class="id" title="abbreviation">erefl</span></a> <span class="id" title="tactic">in</span> <span class="id" title="var">_</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <span class="id" title="var">n</span> := <a class="idref" href="Combi.Combi.stdtab.html#eq_mn:178"><span class="id" title="variable">eq_mn</span></a> <span class="id" title="keyword">return</span> <a class="idref" href="Combi.Combi.stdtab.html#stdtabsh"><span class="id" title="record">stdtabsh</span></a> <a class="idref" href="Combi.Combi.stdtab.html#n:181"><span class="id" title="variable">n</span></a> <span class="id" title="tactic">in</span> <a class="idref" href="Combi.Combi.stdtab.html#t:179"><span class="id" title="variable">t</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="val_stdtabshcast" class="idref" href="#val_stdtabshcast"><span class="id" title="lemma">val_stdtabshcast</span></a> <a id="m:182" class="idref" href="#m:182"><span class="id" title="binder">m</span></a> <a id="n:183" class="idref" href="#n:183"><span class="id" title="binder">n</span></a> (<a id="eq_mn:184" class="idref" href="#eq_mn:184"><span class="id" title="binder">eq_mn</span></a> : <a class="idref" href="Combi.Combi.stdtab.html#m:182"><span class="id" title="variable">m</span></a> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <a class="idref" href="Combi.Combi.stdtab.html#n:183"><span class="id" title="variable">n</span></a>) <a id="t:185" class="idref" href="#t:185"><span class="id" title="binder">t</span></a> :<br/>
<span class="id" title="abbreviation">val</span> (<a class="idref" href="Combi.Combi.stdtab.html#stdtabshcast"><span class="id" title="definition">stdtabshcast</span></a> <a class="idref" href="Combi.Combi.stdtab.html#eq_mn:184"><span class="id" title="variable">eq_mn</span></a> <a class="idref" href="Combi.Combi.stdtab.html#t:185"><span class="id" title="variable">t</span></a>) <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <span class="id" title="abbreviation">val</span> <a class="idref" href="Combi.Combi.stdtab.html#t:185"><span class="id" title="variable">t</span></a>.<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="conj_stdtabsh_bij" class="idref" href="#conj_stdtabsh_bij"><span class="id" title="lemma">conj_stdtabsh_bij</span></a> <a id="sh:186" class="idref" href="#sh:186"><span class="id" title="binder">sh</span></a> : <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrfun.html#bijective"><span class="id" title="inductive">bijective</span></a> (@<a class="idref" href="Combi.Combi.stdtab.html#conj_stdtabsh"><span class="id" title="definition">conj_stdtabsh</span></a> <a class="idref" href="Combi.Combi.stdtab.html#sh:186"><span class="id" title="variable">sh</span></a>).<br/>
<br/>
<span class="id" title="keyword">Lemma</span> <a id="card_stdtabsh_conj_part" class="idref" href="#card_stdtabsh_conj_part"><span class="id" title="lemma">card_stdtabsh_conj_part</span></a> (<a id="sh:187" class="idref" href="#sh:187"><span class="id" title="binder">sh</span></a> : <a class="idref" href="Combi.Combi.partition.html#intpart"><span class="id" title="record">intpart</span></a>) :<br/>
<span class="id" title="notation">#|</span><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#fa3b33ae9d0a52de608b305a09f3b881"><span class="id" title="notation">{:</span></a> <a class="idref" href="Combi.Combi.stdtab.html#stdtabsh"><span class="id" title="record">stdtabsh</span></a> (<a class="idref" href="Combi.Combi.partition.html#conj_part"><span class="id" title="definition">conj_part</span></a> <a class="idref" href="Combi.Combi.stdtab.html#sh:187"><span class="id" title="variable">sh</span></a>)<a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#fa3b33ae9d0a52de608b305a09f3b881"><span class="id" title="notation">}</span></a><span class="id" title="notation">|</span> <a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span class="id" title="notation">=</span></a> <span class="id" title="notation">#|</span><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#fa3b33ae9d0a52de608b305a09f3b881"><span class="id" title="notation">{:</span></a> <a class="idref" href="Combi.Combi.stdtab.html#stdtabsh"><span class="id" title="record">stdtabsh</span></a> <a class="idref" href="Combi.Combi.stdtab.html#sh:187"><span class="id" title="variable">sh</span></a><a class="idref" href="http://rocq-prover.org/doc/V9.1.1/stdlib//Corelib.ssr.ssrbool.html#fa3b33ae9d0a52de608b305a09f3b881"><span class="id" title="notation">}</span></a><span class="id" title="notation">|</span>.<br/>
<br/>
#[<span class="id" title="var">export</span>] <span class="id" title="keyword">Hint</span> <span class="id" title="keyword">Resolve</span> <span class="id" title="var">stdtabnP</span> <span class="id" title="var">stdtabshP</span> : <span class="id" title="var">core</span>.<br/>
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