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<span class="kw">let </span><font color="Maroon" title="c1">a</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</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">  for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">m</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds   <a href="ordinal7.html#K4" title="ORDINAL7:func.4">CantorNF</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p3">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> (<a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>,<font color="Maroon" title="c1">a</font>)</span>)</span></span>)</span> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Olive" title="b2">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p3">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> (<a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>,<font color="Maroon" title="c1">a</font>)</span>)</span></span>)</span>,<font color="Olive" title="b2">m</font></span><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">%&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">n</font>, <font color="Maroon" title="c3">m</font> be   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <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="ordinal7.html#K4" title="ORDINAL7:func.4">CantorNF</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p3">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> (<a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>,<font color="Maroon" title="c1">a</font>)</span>)</span></span>)</span> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p3">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> (<a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>,<font color="Maroon" title="c1">a</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c3">m</font></span><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">%&gt;</a></span></span><br/>



<a NAME="E1:97"/>
 <a href="ordinal5.html#K4" title="ORDINAL5:func.4">Sum^</a> <span class="p1"><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p3">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> (<a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>,<font color="Maroon" title="c1">a</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c3">m</font></span><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">%&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p2">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> (<a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>,<font color="Maroon" title="c1">a</font>)</span>)</span></span>)</span> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c3">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal7.html#T12" target="_self" onmouseover="rs('ordinal7/T12')" onmouseout="rh()">Th25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:97"/>
 <a href="ordinal7.html#K4" title="ORDINAL7:func.4">CantorNF</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p3">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> (<a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>,<font color="Maroon" title="c1">a</font>)</span>)</span></span>)</span> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p3">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> (<a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>,<font color="Maroon" title="c1">a</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c3">m</font></span><a href="afinsq_1.html#K6" title="AFINSQ_1:func.6">%&gt;</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/>


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