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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">Y</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">t</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>







<b>assume </b><a NAME="E1:74"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<font color="Maroon">t</font> <a href="mathmorp.html#K7" target="_self">(.)</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="mathmorp.html#K6" target="_self">(o)</a> <font color="Maroon">Y</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="mathmorp.html#K7" target="_self">(.)</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">Y</font></span>)</span></span>)</span> <a href="mathmorp.html#K3" target="_self">(-)</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="mathmorp.html#K7" target="_self">(.)</a> <font color="Maroon">Y</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="mathmorp.html#K7" target="_self">(.)</a> <font color="Maroon">X</font></span>)</span> <a href="mathmorp.html#K4" target="_self">(+)</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="mathmorp.html#K7" target="_self">(.)</a> <font color="Maroon">Y</font></span>)</span></span>)</span> <a href="mathmorp.html#K3" target="_self">(-)</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="mathmorp.html#K7" target="_self">(.)</a> <font color="Maroon">Y</font></span>)</span>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E3:74"/>
<font color="Maroon">t</font> <a href="mathmorp.html#K7" target="_self">(.)</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="mathmorp.html#K6" target="_self">(o)</a> <font color="Maroon">Y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="mathmorp.html#K7" target="_self">(.)</a> <font color="Maroon">X</font></span>)</span> <a href="mathmorp.html#K6" target="_self">(o)</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="mathmorp.html#K7" target="_self">(.)</a> <font color="Maroon">Y</font></span>)</span>
 ;<br/>


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