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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">b</font> implies  <a href="ordinal5.html#K2" title="ORDINAL5:func.2">first_epsilon_greater_than</a> <font color="Maroon" title="c1">a</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="ordinal5.html#K2" title="ORDINAL5:func.2">first_epsilon_greater_than</a> <font color="Maroon" title="c2">b</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:51"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
<font color="Maroon" title="c1">a</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="ordinal5.html#K2" title="ORDINAL5:func.2">first_epsilon_greater_than</a> <font color="Maroon" title="c1">a</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="ordinal5.html#K2" title="ORDINAL5:func.2">first_epsilon_greater_than</a> <font color="Maroon" title="c2">b</font></span><br/>

<a NAME="E2:51"/>
<font color="Maroon" title="c2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal5.html#K2" title="ORDINAL5:func.2">first_epsilon_greater_than</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal5.html#D6" target="_self" title="ORDINAL5:def.6">Def6</a></span>;<br/>
<a NAME="E3:51"/><span class="kw">then </span>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal5.html#K2" title="ORDINAL5:func.2">first_epsilon_greater_than</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="ordinal1.html#T12" title="ORDINAL1:th.12">ORDINAL1:12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:51"/>
 <a href="ordinal5.html#K2" title="ORDINAL5:func.2">first_epsilon_greater_than</a> <font color="Maroon" title="c1">a</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="ordinal5.html#K2" title="ORDINAL5:func.2">first_epsilon_greater_than</a> <font color="Maroon" title="c2">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal5.html#D6" target="_self" title="ORDINAL5:def.6">Def6</a></span>; <a class="txt" 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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