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<b>let </b><font color="Maroon" title="c1">r</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c2">s</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>



<b>reconsider </b><font color="Maroon" title="c3">r</font> = <font color="Maroon" title="c1">r</font>, <font color="Maroon" title="c4">s</font> = <font color="Maroon" title="c2">s</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <b>by </b><i><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/>
<font color="Maroon" title="c4">s</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p1"><a href="jordan2b.html#K2" title="JORDAN2B:func.2">|[</a><span class="default"><font color="Maroon" title="c3">r</font></span><a href="jordan2b.html#K2" title="JORDAN2B:func.2">]|</a></span> = 
<font color="Maroon" title="c4">s</font> <a href="rvsum_1.html#K11" title="RVSUM_1:func.11">*</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">r</font></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span>

<br/>.= 
<span class="p1"><a href="jordan2b.html#K2" title="JORDAN2B:func.2">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c3">r</font></span>)</span></span><a href="jordan2b.html#K2" title="JORDAN2B:func.2">]|</a></span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T69" title="RVSUM_1:th.69">RVSUM_1:69</a></i>
;<br/>
<b>hence </b><a NAME="E3:27"/>
<font color="Maroon" title="c2">s</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p1"><a href="jordan2b.html#K2" title="JORDAN2B:func.2">|[</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="jordan2b.html#K2" title="JORDAN2B:func.2">]|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="jordan2b.html#K2" title="JORDAN2B:func.2">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c1">r</font></span>)</span></span><a href="jordan2b.html#K2" title="JORDAN2B:func.2">]|</a></span>
 ;<br/>


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