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<span class="kw">let </span><font color="Maroon" title="c1">b</font>, <font color="Maroon" title="c2">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"> ( <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <font color="Maroon" title="c1">b</font> <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> <font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:88"/><span class="lab"><font color="Green" title="E63">A1</font></span>: 
<a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <font color="Maroon" title="c1">b</font> <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> <font color="Maroon" title="c2">a</font>
 ; <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="c1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font></span><br/>

<a NAME="E2:88"/><span class="kw">then </span>
 <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <font color="Maroon" title="c2">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#T33" title="ORDINAL1:th.33">ORDINAL1:33</a></span>;<br/>
<a NAME="E3:88"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A3</font></span>: 
 <a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <font color="Maroon" title="c1">b</font></span>)</span></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<span class="p1">(<span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <font color="Maroon" title="c2">a</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal4.html#T27" title="ORDINAL4:th.27">ORDINAL4:27</a></span>;<br/>
<a NAME="E4:88"/><span class="lab"><font color="Green" title="E65">A4</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">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:88"><span class="lab"><font color="Green" title="E63">A1</font></span></a>, <a class="ref" href="ordinal5.html#D10" target="_self" title="ORDINAL5:def.10">EXP</a></span>;<br/>
<a NAME="E5:88"/>
<font color="Maroon" title="c1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <font color="Maroon" title="c1">b</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal5.html#T57" target="_self" title="ORDINAL5:th.57">Th41</a></span>;<br/>
<a NAME="E6:88"/><span class="kw">then </span>
( <font color="Maroon" title="c1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<span class="p1">(<span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <font color="Maroon" title="c2">a</font></span>)</span> &amp;  <a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> ,<span class="p1">(<span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">a</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:88"><span class="lab"><font color="Green" title="E64">A3</font></span></a>, <a class="txt" href="#E4:88"><span class="lab"><font color="Green" title="E65">A4</font></span></a>, <a class="ref" href="ordinal5.html#D10" target="_self" title="ORDINAL5:def.10">EXP</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:88"/>
<font color="Maroon" title="c1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font>
 ; <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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