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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="sub_metr.html#NM1">PseudoMetricSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:6"/><i><font color="Green">E5</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="metric_2.html#R3" target="_self">tolerates</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="metric_2.html#R3" target="_self">tolerates</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<a NAME="E2:6"/><b>then </b><i><font color="Green">E6</font></i>: 
 <a href="metric_1.html#K4">dist</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="metric_2.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E3:6"/>
 <a href="metric_1.html#K4">dist</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="metric_2.html#E1:6"><i><font color="Green">E5</font></i></a>, <a class="ref" href="metric_2.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E4:6"/><b>then </b>
 <a href="metric_1.html#K4">dist</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 <a href="xcmplx_0.html#K2">+</a> 0
 
<b>by </b><i><a class="txt" href="metric_2.html#E2:6"><i><font color="Green">E6</font></i></a>, <a class="ref" href="metric_1.html#T4">METRIC_1:4</a></i>;<br/>
<a NAME="E5:6"/><b>then </b>
 <a href="metric_1.html#K4">dist</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="metric_1.html#T5">METRIC_1:5</a></i>;<br/>
<b>hence </b><a NAME="E6:6"/>
<font color="Maroon">c<sub>2</sub></font> <a href="metric_2.html#R3" target="_self">tolerates</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="metric_2.html#D1" target="_self">Def1</a></i>;<br/>


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