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<b>let </b><font color="Maroon">r1</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">r2</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">r1'</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">r2'</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>







<a NAME="E1:1"/>
( <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><font color="Maroon">r1</font>,<font color="Maroon">r2</font></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">r1</font> &amp; <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><font color="Maroon">r1</font>,<font color="Maroon">r2</font></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">r2</font> &amp; <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><font color="Maroon">r1'</font>,<font color="Maroon">r2'</font></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">r1'</font> &amp; <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><font color="Maroon">r1'</font>,<font color="Maroon">r2'</font></span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">r2'</font> )
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<b>hence </b><a NAME="E2:1"/>
( <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><font color="Maroon">r1</font>,<font color="Maroon">r2</font></span><a href="euclid.html#K23">]|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><font color="Maroon">r1'</font>,<font color="Maroon">r2'</font></span><a href="euclid.html#K23">]|</a></span> implies ( <font color="Maroon">r1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r1'</font> &amp; <font color="Maroon">r2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r2'</font> ) )
 ;<br/>


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