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<span class="kw">let </span><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">A</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C</font> implies  <a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <font color="Maroon" title="c1">C</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c2">A</font></span>)</span> )</span><br/>



<a NAME="E1:31"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
1 <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> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal2.html#T56" title="ORDINAL2:th.56">ORDINAL2:56</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:31"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <font color="Maroon" title="c1">C</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c2">A</font></span>)</span></span><br/>

<a NAME="E3:31"/><span class="kw">then </span>
 <a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C</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> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="ordinal4.html#T22" target="_self" title="ORDINAL4:th.22">Th22</a>, <a class="ref" href="ordinal2.html#T57" title="ORDINAL2:th.57">ORDINAL2:57</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:31"/>
 <a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> <font color="Maroon" title="c1">C</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c2">A</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal2.html#T61" title="ORDINAL2:th.61">ORDINAL2:61</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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