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<b>let </b><font color="Maroon">M</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="metric_1.html#L1">MetrStruct</a> , <font color="Maroon">N</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="metric_1.html#L1">MetrStruct</a> ;<br/><b>let </b><font color="Maroon">m1</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">M</font>, <font color="Maroon">m2</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">M</font>;<br/><b>let </b><font color="Maroon">n1</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">N</font>, <font color="Maroon">n2</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">N</font>;<br/>





<b>consider </b><font color="Maroon">x1</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">M</font>, <font color="Maroon">y1</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">M</font>, <font color="Maroon">x2</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">N</font>, <font color="Maroon">y2</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">N</font><b> such that </b><br/><a NAME="E2:23"/><i><font color="Green">E46</font></i>: 
( <span class="p1"><a href="topreal7.html#K2" target="_self">[</a><span class="default"><font color="Maroon">m1</font>,<font color="Maroon">n1</font></span><a href="topreal7.html#K2" target="_self">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="topreal7.html#K2" target="_self">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font></span><a href="topreal7.html#K2" target="_self">]</a></span> &amp; <span class="p1"><a href="topreal7.html#K2" target="_self">[</a><span class="default"><font color="Maroon">m2</font>,<font color="Maroon">n2</font></span><a href="topreal7.html#K2" target="_self">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="topreal7.html#K2" target="_self">[</a><span class="default"><font color="Maroon">y1</font>,<font color="Maroon">y2</font></span><a href="topreal7.html#K2" target="_self">]</a></span> )
 <b>and </b><br/><a NAME="E3:23"/><i><font color="Green">E47</font></i>: 
the <a href="metric_1.html#U1">distance</a> of <span class="p1">(<span class="default"><a href="topreal7.html#K1" target="_self">max-Prod2</a> <font color="Maroon">M</font>,<font color="Maroon">N</font></span>)</span> <a href="metric_1.html#K1">.</a> <span class="p1"><a href="topreal7.html#K2" target="_self">[</a><span class="default"><font color="Maroon">m1</font>,<font color="Maroon">n1</font></span><a href="topreal7.html#K2" target="_self">]</a></span>,<span class="p1"><a href="topreal7.html#K2" target="_self">[</a><span class="default"><font color="Maroon">m2</font>,<font color="Maroon">n2</font></span><a href="topreal7.html#K2" target="_self">]</a></span> <a href="hidden.html#R1">=</a>  <a href="square_1.html#K2">max</a> <span class="p1">(<span class="default">the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">M</font> <a href="metric_1.html#K1">.</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p1">(<span class="default">the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">N</font> <a href="metric_1.html#K1">.</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font></span>)</span>
 <b>by </b><i/>;<br/>
<a NAME="E4:23"/>
( <font color="Maroon">m1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">n1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> &amp; <font color="Maroon">m2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">n2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> )
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<b>hence </b><a NAME="E5:23"/>
 <a href="metric_1.html#K2">dist</a> <span class="p1"><a href="topreal7.html#K2" target="_self">[</a><span class="default"><font color="Maroon">m1</font>,<font color="Maroon">n1</font></span><a href="topreal7.html#K2" target="_self">]</a></span>,<span class="p1"><a href="topreal7.html#K2" target="_self">[</a><span class="default"><font color="Maroon">m2</font>,<font color="Maroon">n2</font></span><a href="topreal7.html#K2" target="_self">]</a></span> <a href="hidden.html#R1">=</a>  <a href="square_1.html#K2">max</a> <span class="p1">(<span class="default"><a href="metric_1.html#K2">dist</a> <font color="Maroon">m1</font>,<font color="Maroon">m2</font></span>)</span>,<span class="p1">(<span class="default"><a href="metric_1.html#K2">dist</a> <font color="Maroon">n1</font>,<font color="Maroon">n2</font></span>)</span>
 <b>by </b><i/>;<br/>


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