<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">C</font> be   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>   non  <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a>   non  <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds   <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">n</font>)</span>)</span> <a href="finseq_6.html#K7" title="FINSEQ_6:func.7">^'</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">n</font>)</span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="finseq_6.html#K7" title="FINSEQ_6:func.7">^'</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span><br/>



<a NAME="E1:16"/>
 <a href="finseq_6.html#K1" title="FINSEQ_6:func.1">Rotate</a> (<span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <span class="p2">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="finseq_6.html#K7" title="FINSEQ_6:func.7">^'</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1e.html#T11" target="_self" onmouseover="rs('jordan1e/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:16"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1" title="JORDAN9:func.1">Cage</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan1e.html#K1" title="JORDAN1E:func.1">Upper_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="finseq_6.html#K7" title="FINSEQ_6:func.7">^'</a> <span class="p2">(<span class="default"><a href="jordan1e.html#K2" title="JORDAN1E:func.2">Lower_Seq</a> (<font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="revrot_1.html#T33" onmouseover="rs('revrot_1/T33')" onmouseout="rh()">REVROT_1:33</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
