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<span class="kw">let </span><font color="Maroon" title="c1">b</font> be   <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">n</font> being  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">n</font> holds <br/><span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> is  <a href="ordinal5.html#V6" title="ORDINAL5:attr.6">Cantor-normal-form</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">n</font> be   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">n</font> implies <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> is  <a href="ordinal5.html#V6" title="ORDINAL5:attr.6">Cantor-normal-form</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:92"/><span class="lab"><font color="Green" title="E65">A0</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> is  <a href="ordinal5.html#V6" title="ORDINAL5:attr.6">Cantor-normal-form</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">A</font> = <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>;<br/>
<a NAME="E2:92"/><span class="lab"><font color="Green" title="E66">A1</font></span>: 
(  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p1">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#D5" title="AFINSQ_1:def.5">AFINSQ_1:def 5</a></span>;<br/>
<div><span class="kw">hereby </span> <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="ordinal5.html#D11" target="_self" title="ORDINAL5:def.11">ORDINAL5:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> holds <br/><a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <span class="p1">(<span class="default"><span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p4">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <span class="p1">(<span class="default"><span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p4">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font></span>)</span></span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c4">a</font> be   <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> implies <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">a</font> is  <a href="ordinal5.html#V5" title="ORDINAL5:attr.5">Cantor-component</a>  )</span><br/><span class="kw">assume </span><a NAME="E1:92_1"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">a</font> is  <a href="ordinal5.html#V5" title="ORDINAL5:attr.5">Cantor-component</a> </span><br/><a NAME="E2:92_1"/><span class="kw">then </span>
( <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:92"><span class="lab"><font color="Green" title="E66">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a>, <a class="ref" href="ordinal3.html#T18" title="ORDINAL3:th.18">ORDINAL3:18</a></span>;<br/><span class="kw">hence </span><a NAME="E3:92_1"/>
<span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">a</font> is  <a href="ordinal5.html#V5" title="ORDINAL5:attr.5">Cantor-component</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:92"><span class="lab"><font color="Green" title="E65">A0</font></span></a>, <a class="txt" href="#E2:92"><span class="lab"><font color="Green" title="E66">A1</font></span></a>, <a class="ref" href="ordinal5.html#D9" target="_self" title="ORDINAL5:def.9">CC</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be   <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">b</font> &amp; <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> implies <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <span class="p1">(<span class="default"><span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p4">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <span class="p1">(<span class="default"><span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p4">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">a</font></span>)</span> )</span><br/>



<span class="kw">assume </span><a NAME="E4:92"/><span class="lab"><font color="Green" title="E67">A2</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> or <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <span class="p1">(<span class="default"><span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p4">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <span class="p1">(<span class="default"><span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p4">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">a</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E5:92"/>
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&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#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <span class="p1">(<span class="default"><span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p4">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <span class="p1">(<span class="default"><span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p4">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">a</font></span>)</span></span><br/>

<span class="kw">hence </span><a NAME="E6:92"/>
<a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <span class="p1">(<span class="default"><span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p4">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <span class="p1">(<span class="default"><span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <span class="p4">(<span class="default"><a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<font color="Maroon" title="c1">b</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:92"><span class="lab"><font color="Green" title="E67">A2</font></span></a>, <a class="txt" href="#E2:92"><span class="lab"><font color="Green" title="E66">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a>, <a class="ref" href="ordinal3.html#T18" title="ORDINAL3:th.18">ORDINAL3:18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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